Full form of fps

First-person Shooter: a shooting game where you see the world as your character does. Examples include Call of Duty, Halo and Counter-Strike.
First-person Sneaker: Similar, but the focus of the game is more on stealth.
Frames per second: The number of times a game engine can redraw the game screen in one second. Optimal values can be anything from 24 to 60, depending on the game.