Epidermis forms the outermost layer of the skin. It contains keratin which is a protein that moistens skin and hair. The outermost layer of the epidermis constitutes dead keratin cells and is called stratum corneum.
When the skin of toes and fingers are kept in contact with water for a long time, this layer of dead keratin cells expand and become puffy. But there is layer of living keratin cells which resides below the dead layer, which has no space left after the expansion. So the stratum corneum becomes wrinkled to give them some space.