The speed of a lens and how ‘fast’ it is refers to the maximum aperture of the lens. The larger the maximum aperture the faster the lens is.
When a lens is talked about it generally is described with its focal length (for example it could e a 50mm lens or a 300mm lens) as well as its maximum aperture (usually it will be a number with an ‘f’ in front of it – for example f/1.8 or f/4 or f/5.6). The smaller the number is the bigger the maximum aperture is.
Remember that aperture is the size of the hole in the lens that lets light in when you hit the shutter. So the bigger the maximum aperture – the more light that your lens will allow in.
The reason that a lens with a big maximum aperture is referred to as fast is that it lets more light in and therefore you can use faster shutter speeds even when there might not be much light around.
Why would you want a fast lens?
Fast lenses can be advantageous over slower ones in certain shooting conditions and types of photography. They really come into their own where there is either low light (for example if you need to shoot indoors but can’t use a flash) or where you need to use a fast shutter speed (for example in sports or even wildlife photography). They are especially useful when you need both a fast shutter speed in low light (ie indoor sports).
Keep in mind also that because you’re using larger apertures that this has an impact upon the depth of field that you get in your shots. Larger apertures lead to shallower depth of field which can be a great thing if you’re wanting to make your subject really stand out from its background.
Fast lenses can be really useful to have but unfortunately they can also be quite expensive to buy. However if you’d like a more economical fast lens you might like to check out 50mm lenses. For example both Nikon and Canon have some lovely fast lenses in this focal length.