So that’s the quick, generic answer. More technically, there is a waxy/oily substance your skin secretes from the sebaceous glands called “sebum”. In these glands, sebum is produced within special cells and is then secreted when these cells burst.
This substance, among other benefits, has the dual effect of helping your skin and hair stay hydrated underneath, so it doesn’t get dry and cracked, while also helping to protect your skin from excess moisture from the outside. You will have probably noticed sebum at some point in your hair if you go a couple days without washing it. Your hair will start to feel very oily when you run your hands through it. When you are in water for extended periods, this sebum gets washed away from your skin and hair, removing this protective layer.
Now you might be wondering why only your finger tips and toes get wrinkly and not the rest of your body (or at least not nearly as fast). The reason why is not 100% understood, but we do have a pretty good idea of what is going on here. The skin’s outermost layer, the epidermis, contains a protein called keratin. This protein helps strengthen your skin.
Dead keratin cells also make up the epidermis’ surface layer, called the stratum corneum (Latin for ‘horny layer’, funny enough). So once all the protective sebum is washed away, these dead keratin cells absorb the water like a sponge and swell. This is why your skin is much easier to cut or break when it is waterlogged. The strong outer layer of dead keratin cells loses some of its toughness when waterlogged.
The reason then that your toes and fingers get more wrinkly is that they contain a thicker layer of both living and dead keratin cells than the rest of your body. This causes them to swell more noticeably then the rest of your skin as the dead keratin cells absorb water.
The wrinkle effect occurs, rather than just general swelling, because the inner layer of living keratin cells stays more or less the same as it was before you were in the water, while the outer layer swells; the connections between these two layers stay closely bonded while the places not connected are free to swell, hence, the pruney fingers and toes.