It's the tissues getting waterlogged. Skin is waterproof to an extent, but eventually water soaks in. They go wrinkly because skin isn't evenly "stuck" to what's beneath it, some areas are more firmly attached than others so the skin doesn't expand evenly.
The other reason is that skin isn't an even thickness either, so it will take up more water in some areas than others. (Would have posted this last night but PC misbehaved.)