The reason is this:
The eye detects movement, or the lack of it.
The ear also is capable of detecting movement. Deep within the recesses of your ear there is a liquid used by the brain to detect movement. Whenever there is movement, that liquid sloshes around in your ear, letting your brain know that "hey, I'm moving!"
The problem is when you play games like FPSs: While your eyes are telling your brain "wow, I'm jumping around and ducking rockets", your ear is telling your brain, "what movement? You're standing still!"
Confusion in your brain ensues, promising a very nauseating time.
The same phenomenon happens with ships (albeit in reverse). You get seasick because the liquid in your ear is sloshing around, but your eyes, fixated on the horizon, do not detect movement.
If you get seasick, chances are you will get "FPS-sick".
And no, although a slight percentage of the global population does, I don't suffer from this.
