Consider the exposure triangle - aperture, shutter speed and ISO. When you adjust one, you can adjust the others accordingly. Ignore ISO for now, as that is a function of the camera, and consider the aperture and shutter speed variables.
The wider the aperture, the more light can enter the camera. This means that for any given exposure, the shutter speed can be shorter - in other words, the shutter speed is fast. Faster shutter speeds are generally desirable as they freeze motion and counteract camera shake.
So a fast lens is generally a wide aperture lens, like a 1.4 or 2.8, because compared to a slow lens like a 4 or 5.6, you can get many more shutter speed stops with them.