The term fast could also refer to the lens being able to let in more light (due to large aperture)....hence allowing the exposure time shorter (allowing...faster shutter speeds) for a given desired exposure.
...which translate to a smaller margin of error in focussing. For example, the AF logic may choose to focus on the neck when you want a sharp focus on the eye. Because of a shallow DOF, the neck area will be sharp but the eye area will be out of focus.
However, it comes in very handy in low-light conditions where sometimes you can get away with a sharp picture (no handshake blur) without using a tripod.
BUT...fast lenses are usually big, heavy and expensive (perhaps the only odd exception is the 50mm prime lens).
A good fast lens is the 50mm 1.8 canon btw...........Im not sure what its equal would be in nikon.
A f/2-3 (somewhere between 2 and 3) is going to be a plus when shooting sports. Most all non brand lens are going to be F5 and up, imposisble to shoot sports other than in braud daylight and 400iso or higher.