FPS stands for "frames per second." It is used to measure how many frames are captured in a second.
In still photography it refers to how many images can be captured in a burst. For example, if a camera is put in high burst mode and can capture seven frames per second, it means that every second that the shutter button is depressed, seven frames will be captured.
In video, FPS refers to frame rate. These will be much higher numbers than when discussing a camera's burst rate. The frame rate determines the look of the footage and what can be done with it. Faster frame rates of 60 FPS and higher are ideal for capturing slow motion footage.