Some of the cells in the skin of your fingers, called "keratinocytes", self-destruct naturally while your skin is developing. This causes the development of layers of cell membrane and keratin-rich cellular components in your skin. When your hands get wet for a long time, moisture is able to get into these layers if any openings are exposed (very normal due to how skin wears out) and is absorbed by the keratin-rich molecules. This causes a temporary swelling of these layers. The skin above it then starts to wrinkle because it's on top of the swelling layers. If left to dry normally, the water will evaporate from the same places that it got into these layers. This is helped by your body-heat essentially burning off the liquid.
Source(s):
http://www.scientificamerican.com/article.cfm?id=why-do-fingers-wrinkle-in
