The term fast lens is attributed to a lens that facilitates the use of a fast shutter speed. Usually, when the lens you are using has a wide open aperture (f/2.8 and above), it is considered a fast lens. Why? Because when a lens opens up wide (big aperture) a lot of light can enter the camera and produce a well-exposed photo even when using a fast shutter speed.
Usually, when the lens opens up wide and lets in a lot of light it is balanced by using a faster shutter speed (Exposure Value, aperture value, and shutter speed). Otherwise, the image will wash out. With fast shutter speed you can literally stop action, a reason why they are popular with action and sports photographers. Additionally, the fact that they can collect a lot of light means you can use them in tackling low light situations as well.