Simply put, they are long pieces of fabric that are attached to the bottom of your skis to give you enough traction to climb upslope during backcountry or cross-country ski adventures. They get their name from the fact that in the beginning some were made using the skin of seals, but for the most part, today’s skins are made from nylon, mohair, or some combination of the two.
They provide traction through the use of tiny fibers or hairs that allow the ski to glide in only one direction. Think of it like petting a dog. If you go with the direction of the hair, your hand will glide over the surface fairly easily. However, if you go against the way the fur naturally grows, your hand is likely to get hindered. In the case of the climbing skins, the snow would be your hand, and the fur would be the fibers of the skin.