The number of pictures a game draws each second. The higher and steadier it is, the smoother the motion and the snappier the controls.
FPS stands for frames per second. A game is really a series of still pictures shown quickly. At sixty frames a second motion looks smooth; thirty is still acceptable for many games; below that, stutter creeps in and the game responds late to the player's input. Steadiness matters more than a high number: a stable rate is easier on the eye than one that jumps up and down.
Frame rate depends on the power of the device and on how many objects and effects are in the scene. 2D games are usually light, while 3D is heavier and its performance depends on the player's device, which is why worlds made in 3D Game Design stay light and stylized. Practical tip: test your game on the weakest device your audience is likely to use, not on your own. If it stutters, reduce the number of objects in the scene before anything else.