He is pretty much the one shot nuke assassin, though his usability is somewhat more geared against intelligence heroes now that they changed his mana burn from the extremely annoying flat (260?) amount to an intelligence based amount.
You run in, break stealth with an attack, stun then mana burn, and you have a kill. Decent hero to get at least a Dagon I on, and great for pub stomping/demoralizing, since it's like facing Predator without the common sense of getting wards.
Great for ganks, but unless you have a lot of farm from hero kills, you fall behind fairly easy. Still, nothing like making a 5v5 teamfight 5v4 by taking out the squishy intelligence support, or possibly a carry.
Not to mention he kinda just dies in a teamfight, being that he's super squishy and melee range. Kinda like Riki in that sense, except without the permanent silence cloud or the neverending stealth to rely on.
So that's kinda his gimmick. Like other people mentioned, he doesn't really get that much scarier late on... kinda peaks at level 11.
If I were to think of other limitations he suffers from, it would be things like:
1. He has no real gap closer... which is kinda horrible for an assassin. He makes up for it with a large number of stuns, but he can have some real trouble catching up to targets he can't kill instantly. This is not helped by his mediocre movespeed and the fact that his item builds have no room at all for movespeed items.
2. His own mana costs are crazy high. A big part of why he's kinda shitty later on is because he needs to devote around half his item pool just to sustain his mana usage. We're looking at mana boots AND bottle level of mana draining. Even then you might even need more mana regen... especially if you ever want to push.
3. He's a pretty crappy laner all things considered... especially if he's up against a strength hero with no intelligence. It's really quite easy to kick him out of the lane so he doesn't get his ultimate until it's too late, since even his base stats alone are very low. Again, it doesn't help that he has the stats of a ranged hero but is melee.
I guess those are the prices you pay for having obscene burst damage.
Tl;dr: Nyx hurts like hell once and can't do anything after that. Also kinda useless later on.