Another thing a bio measures is how into the game you are, and whether the setting provided stimulates your imagination. This, I suppose, is the most relevant function of the bio, as it's better to have players who are actually into the setting and spirit of the thing than ones that are not.
Letting players write their bios often adds to your worlds, too, gives you personal plot hooks and ideas to weave in and makes a stronger bond between GM and player. Even if the GM has the right to not accept these ideas.
Bios made at game start don't have to be absolute, strict rules for your character. You might realize you want to take them into a different direction, personality-wise, or explore some previously unmentioned aspect of their backstory - and I think that's fine. Characters develop, that's only good.
This pretty well sums up my stance on the issue.
A GM for any gaming group wants to attract people who will like the stuff they create; if players decide that the way the game is developing isn't what they thought they'd get from the OP (which as Derm said should indeed have color and style to help avoid this, and I'm pretty sure we already had a conversation in here about what a good OP should bring to the table) then they'll bail on the game, which will probably end it before its time, which is not an eventuality you typically allow knowingly when you're setting up the game in the first place. A well constructed Bio sheet will help the GM find people who will like what the game has to offer in terms of story/setting/interactions.
If a GM is looking for a game where characters develop (or rather, where they will develop independently of the GM putting words in their mouth like they were Barbie dolls in his own private universe,) then they'll be looking for people who will play their characters with more than a single bolded six word action. When the GM is creating a game where they would like the players to supply/create a bit of fluff in each post to enrich the collective game experience and the world, they want to find players who will actually do that; a short description of the character they want to play lets the GM know that the player is willing to put in the effort to write at least that much on behalf of the game.
Or in other words:
This. Honestly, I'd much rather find out about the character as the game progresses. Otherwise it's often just a wall of text contest, with the people putting the most syllables on paper getting in.
Yeah, speaking as a GM, so would I. The thing is, when I ask for a bio I'm not asking for a "wall of text" contest or a "make the wackiest character" contest (well, unless that's the point, anyway) - usually I'm just looking for players who are willing to add a bit of flavor to the pot for everyone to play with, ideally while latching onto some of the color I put in the OP and riffing off of that. Maybe the stuff in the bio never comes up, or the player develops in a way that flat contradicts the original vision; that's fine, and frankly it happens all the time. Even if it wasn't how I originally envisioned that aspect of the setting playing out, if it's cool and interesting I'll roll with it; that's why I'm running a game and not just writing a story myself. I just want to see that you will put that sort of effort into the game when it is appropriate to do so, and that the flavor you contribute will complement what is already in the pot.
I'll be honest, Derm - if it's a game where I'm asking for a bio, it's already not something where I'm looking for you as a player. There's fun to be had in a For Science! or any of the games you mentioned, and your playstyle works wonders in them, but there are also people who like deeper and more thought-out games which benefit from player commitment from the start.
Your assessment and vote of confidence is accurate but hurtful
I wouldn't say it's a bad thing, it just depends on the type of game being created. If I'm creating a fluff-heavy game, then I'm looking to basically do a lot of freeform writing with some parameters beyond my control to give it structure and constraint (in much the same way I'd choose to obey the rules of Haiku or Iambic Pentameter if I were a poet instead.) The more rules I set up at the start, the more control I sacrifice over what I create.
I retain the most control in Minimalist styles, since in those I have maybe some setting rules I set up at the start and then player actions and the capriciousness of the dice- I don't expect a lot of RP or fluff to be supplied by the players, so that's a burden of fluff I accept in exchange for the freedom to put words and feelings in the "mind" of the character, in the void where the player
didn't put them. If I want to write with less control over the game and story, then I give more agency to the players- they get to decide how their characters interact with themselves and their environment through fluff and RP, and at the extreme of that scale I let the players be masters of their domains (e.g if the story fluff calls for the finest dwarven cuisine to be served I don't just fart out Plump Helmets or whatever, I ask the dwarf character what dwarves eat and find a way to weave the answer into the rest of the setting.)
Agency in the story is a responsibility; if I give it to someone who doesn't want it they'll have less fun, and if they don't shoulder that burden then everyone will have less fun. I'd rather know whether the burden of a paragraph of fluff per post is more than you want to deal with before the game starts, and a bio sheet tells me that.
I think we've run into an interesting sub-discussion of "How to Make a Good OP" here- namely...
How to Utilize a Character Application Form
GM
You get the job of creating the Form, which means that it should ask the questions you need to create a good character for your game, and it should provide you with the criteria to evaluate whether a character application is "good" to determine the suitability of both the character and the player for your game. Character Applications commonly contain the following sections:
Identifying Characteristics: This section of the sheet is used to superficially differentiate the player characters from one another. It will be present in almost all character application sheets, unless all players are managing/competing to manage the same character (e.g a Suggestion game.) It typically includes one or more headers for the character's Name, the color (if any) of their speech text, their avatar or image symbol, or any other attribute used to quickly designate a portion of your game as relating to that character.
Game Mechanics: This section of the sheet is used to list the attributes the player selects for their character as they pertain to the specific rules of the game. Any game where players are not equal in the eyes of the game mechanics will have this section, while games where every character plays the same will likely not have this section. It typically includes things like a character's Race/Class combo, their starting Stats or Bonuses, or their Skills or abilities. Anything a player can choose in character creation to change how their character plays or the role they serve in the game falls under this category.
Fluff: This section of the sheet is used by the player to supply the aspects of a character which do not have a mechanical effect on gameplay but which serve as a way to visualize the character and provide an intention of how the character will fit into the story and RP of the game. If you creating a game that will be light on player RP or fluff (because you intend to supply that yourself, or because the game mechanics are the focus, or whatever) you probably don't need an applicant to fill out a detailed bio as part of their character sheet- at most, it is a purely optional bit of spice that gives you an idea how the player would prefer their character be fluffed in game, and shouldn't take precedence over any other portion of the character application sheet. It typically includes things like the character's Biography or backstory, their physical Appearance, their character motivations, or their personality attributes. Anything which affects how a character interacts with the game world without the use of dice or other game mechanics belongs in this category.
Note that these sections are just the information you are trying to get from the player; the method you use to obtain it can vary dramatically. Most Character Application sheets ask for the relevant information with terse categories and blank spaces, which is certainly easy and fast (and entirely appropriate for fluff-light games,) but there are other methods for RP-heavy fare; if you want your applicants to provide information more inspired than that found on a DMV form, you can ask for it in more inspired ways too. You can phrase the categories as a series of questions (perhaps from the Point of View of an in-universe character,) or you can get the information indirectly by asking a different question or positing a hypothetical situation which would allow you to infer the answer you really want to get. Just remember that if you want flavor and creativity from your players, you need to supply some yourself, and the Character Application Sheet is the very first interaction your players will have with your game- don't neglect tone and style here just because you ladled it on in the rest of the OP!
When creating your Character Application Form, it is important to consider a few factors. First, you only need to include the things important on the very first turn of the game; it may be important to know Race and Class at start, but perhaps they do not gain skills or other abilities until later in the game. Similarly, if the backstory of the world is not going to be explored until later in the game, then the character's Biography is also not important since they have no backstory to fit in with until then; it may be more important to know things like Personality attributes or Motivations instead, with the reasons for those attributes being explored as backstory is filled in. And of course, if your game doesn't have any detailed Game Mechanics or won't provide a fertile ground for RP or fluff, you don't need to include those sections- indeed, you shouldn't, so that your priorities are communicated to the players.
Second, the Character Application represents a significant investment in your game for your players, even for short applications. The longer and more detailed the Application, the larger the investment. Large Character Application sheets are appropriate if you want a small number of committed players (e.g if you want four highly developed characters throughout the entire game,) while shorter Character Applications are appropriate if you want many applications for players (e.g if there is a high player mortality rate or many players in the game at the same time.) You may need to compromise if you seek a middle ground; if you want detailed mechanics with smaller player input in the game, for example, you may want to introduce mechanics gradually instead of all at once in the OP, or if you want many players having detailed character interactions you may want to trim other parts of the Character Application or simply focus on the single most important piece of Fluff for your game.
Finally, it is quite likely you are using your Character Application sheet as a method to screen players who want to play your game with you. If you are using an alternate player selection system such as First Come First Served then you only need to verify that the sheets are filled out correctly, but otherwise you need to differentiate between "correct" and "good." A good character sheet should demonstrate that a player has read the entire OP and accepts the tone and style you want the game to create, and that they understand any game rules or mechanics present. Questions about your OP or character sheet are not bad- they show that the player is trying to create a good character, which is exactly what you want! Remember that every part of your Character Application Form should have a purpose; as a general rule, you shouldn't judge characters based on criteria that won't be important during the game.
Player
So, you're looking to join a game, and you see it has a big old Character Application sheet. This is great news! If you're looking to join its because there is something here appealing to you, and you want to play; by adding a Character Application sheet, the GM is telling you exactly how to get in the game.
Before you get into it, try to think about why, exactly, you want to get into this game- you want to make sure that the experience you want to have in this game is the experience the GM is trying to deliver. If you like the game mechanics then check to see that they are well constructed and don't bow to extraneous forces; if you think you can bully the GM into changing the rules on the fly, the rules aren't worth that much to begin with, are they? Conversely, if you read the OP and got excited about the setting or lore, then you want to see whether the Fluff sections of the Character Application sheet are adequately represented; if not, then the GM isn't likely to focus on them as much as you might like, and you'll likely experience less collaboration with other players since they are probably here for other reasons.
If you still think the GM is going to create and perpetuate a game you want to be a part of, then you'll want to make a Character Application Sheet that is as attractive as possible (while still being what you want it to be, of course.) When naming your character, aim for something that will fit the setting; hopefully there will be some names in the OP to give you an idea of the game's nomenclature, but if not you'll have to guess. There are plenty of sites with baby naming suggestions for realistic or modern games, and similarly there are plenty of name generators for more fantastic settings as well. Pick something that will fit with the setting your GM is trying to create; if your GM doesn't seem to care about setting or fluff then you could well get away with using your forum handle, but that will be a big turnoff if the GM is trying to make an immersive Fantasy setting, for example.
If the game has lots of rules and gameplay mechanics, make sure you understand them before filling out that portion of the sheet. Don't be afraid to ask questions; if the GM went to the bother of inventing a whole new game then they knew they would have to teach it to their players, and they'd much rather you be excited to learn about it than complain when your lack of understanding puts you in a bad position later in the game. Many GMs who create intricate rules systems have done so because exploring the possible mechanical interactions is fun on its own, and letting other people play with them reveals aspects of their creation they had not considered. If they enjoy discussing the ramifications of their rules with you during character creation, then they will want you to stick around and play to talk about the situations that arise as the game is played.
If the game has a large fluff component, that is a sign that the GM is giving you agency in the story, and this is your chance to show how you would use that power in the course of play. Communicate effectively; use proper spelling and grammar so it is easy to understand you, and so you seem more intelligent and creative. Try to match or explore the tone or setting elements in the OP that made you interested in this game in the first place; by giving you agency in the story the GM is asking what sorts of things you'd like to interact with, so by showing what is important to you it lets the GM evaluate whether those are the things that are important to them. If there is a Biography then the GM wants you to show you understand the setting and are willing to incorporate those elements into your own character; in other words, if you will take something the GM made and make something new with it. If there is a section about your personality or motivations then the GM wants to see whether your character is dynamic and willing to respond to new developments in interesting ways; in other words, if you'll let the GM take things you make and create new situations for you to interact with.
Remember, the Character Application Sheet is a two way street; it is not just a way for a GM to judge whether you would fit in with the game, but it is also a tool for you to judge what you think the GM will do with the game, and whether the fun the GM and other players are trying to have is an experience you want to be a part of. If you are unclear about what the GM is hoping to accomplish with their game, ask!
...wow, okay, if this was a Wall of Text competition I think I just won