The reflectors come in a variety of surfaces, white, silver and gold are the most usual to see. The idea is to bounce some light into the shadow areas thereby reducing the overall contrast of the shot. By moving closer to the subject or further away you can 'fine tune' the amount of contrast very accurately.
The opposite piece of kit, which is black and is used in the same way but to reflect black onto the subject, creating shaded areas, is called a gobo.
Gobos and reflectors are used a lot in fashion and glamour photography.
Although reflectors and gobos are probably not a practical proposition for all but the most dedicated amateur photographers, it is worth understanding how they are used. Quite often you can find a white wall, or use a piece of card or paper, to do the same job.