There are various theories of why fingers and toes wrinkle in water. Most biologists suggest that the tough outer layer of skin made up of dead keratin cells is responsible. Keratin is a protein found in hair, nails, and the outermost layer of our skin.
Our skin is made up of three layers:
The epidermis is made up of four layers:
The stratum corneum is the outer layer of our skin - the part that we can see and feel. This is the layer with the dead keratin cells.
While a person is in the pool or a bathtub for a long time, the dead keratin cells absorb water. This absorption causes the surface area of the skin to swell, but the outer layer is tightly attached to the living tissue. So, to compensate for the increased surface area, our skin wrinkles.
So why does this happen to hands and feet and not to other parts of the body? Because the hands and feet have the thickest layer of dead keratin cells. Our hands and feet are subjected to a lot of wear and tear. Imagine if the palm of our hands had skin as thin as that on our backs. No fun playing basketball with skin that thin!
Source: http://www.loc.gov/rr/scitech/mysteries/wrinkles.html