I searched for Heroes of Might and Magic III on these forums after playing it for a little while. What I found shocked me: the thread died.
Don't worry. I'm fixing it. Now.
HoMM3 is highly regarded as many to be one of the best TBS games ever created, some still playing it to this day, some claiming it is the best game of all time. Reviewers and players praised its balance, replayability and unit diversity, as well as enjoyability and grand strategy > gigantic unit ball of death. But you all know that.
What's that? "I have never played HoMM3" I hear 1% of the forum screaming? Your actually reading this now? This is madness! You will all be educated you sick minded pheasants!
HoMM3 is simply a game where you start with a single town (or possibly more) and your job is to win the game by completing the scenario objectives. There is your classic kill the other dude, but there is also capturing artifacts, destroying a certain NPC within a certain amount of turns, or whatever the mission asks you to do. Strategies are endless, potential is unlimited!
After selecting a map and faction, you are thrown into the land of Might and Magic, where there is Magic and... Might. You tend to start with your hero plus a basic starting army. Your army is created in your city, by training more troops at the end of a week (7 turns) and by upgrading your city, you can increase the diversity of your troops, giving you plenty of ways to mix and match unit combos to suit your needs and playstyle.
And here the Magic begins (errr... and Might). Your hero can have artifacts/items that he can use throughout his lifespan, and he will also level up and gain stats. A powerful hero is a good hero, one good hero can wipe the floor with a weak hero backed by a strong army. As such, leveling your hero is of utmost importance, and defending him is just as important.
When a hero does level up, he gains a point in a stat (out of 4), and then gets to choose between either upgrading a secondary stat (like increased map movement, magic power etc) or gaining a new one entirely, eventually maxing out at a certain number or secondary skills. This allows skillful and thoughtful, although random, customization. Yes, it may seem like luck, but often you will find that when you hire heroes (cause having just 1 isn't fun enough) they will have the starting stats you want, so you can just upgrade them all day long.
Combat in the game takes place in battlegrounds where two entities meet, as shown above. Each player takes turns using the units depending on speed ratings, and there are many options as to what you can do with those units. You can get them to defend, wait (so they can be used later in the turn, which is actually very useful) or you can attack with them. Alternatively, you can use a hero spell. These spells are battlechangers, tipping the tides in even battles and giving you the upper hand. Magic spells have various effects, dealing damage or buffing a friendly unit are the most common. Some are not used in battle however.
Maybe I should stop writing now. Maybe you should start playing. Go grab it on GOG and maybe we could get a bay 12 game/tourney going (If that is even still possible with this game. It would be pretty fun. This game was also very highly praised for the multiplayer)