A fast lens refers to it's maximum aperture. Zoom lenses f2.8 would be considered a fast lens. In a prime lens(fixed focal length) it depends on the focal length. Longer lenses like a 200mm or larger f2.8 is fast. With shorter focal length lenses f1.8, f1.4 would be considered fast.
These large apertures will allow you to shoot in lower light than slower lenses as they gather more light. Generally speaking the faster the lens the higher the cost as well and with lenses you get what you pay for.
You may want to read up on photography in general and learn the basics of exposure. Learn how shutter speeds, apertures and ISO's work and work together. It is really not too complicated once you get your mind wrapped around the basics of exposure.