Why Do Your Fingers and Toes Wrinkle During a Bath or Underwater?
For a long time, people thought the water caused the skin to swell up and get puffy. Now researchers believe wrinkly fingers could be an autonomic nervous system reaction. Because it's easier to pick up wet objects with wrinkly fingers.
Wrinkles on your fingers may give you more grip, kind of like treads on a car tire.
The epidermis, or outer layer of the skin, is made up of cells called keratinocytes, which form a very strong intracellular skeleton made up of a protein called keratin. So when hands are soaked in water, the keratin absorbs it and swells. The inside of the fingers, however, does not swell. As a result, there is relatively too much stratum corneum and it wrinkles, just like a gathered skirt. (The hair and nails, which contain different types of keratin, also absorb some water. This is why the nails get softer after bathing or doing the dishes.)

So, when you keep your hands in water for a long time then your body will stop making new cells and within 10 minutes of being in the water you will start getting wrinkles and after 3–4 weeks your hand, it would become a soap-like a substance called "grave wax".
Laboratory tests confirmed a theory that wrinkly fingers improve our grip on wet or submerged objects, working to channel away from the water. In fact, the distinctive wrinkling is caused by blood vessels constricting below the skin.
By Todd R. Nelson MD.
Researchers noticed that it didn’t happen to people with nerve damage to the fingertips or toes.
That meant the wrinkling was part of an involuntary (automatic) response of the nervous system. Pruney fingers and toes are actually caused when blood vessels just below the skin shrink — a process called vasoconstriction. When your nervous system is functioning properly, soaking in water sends a message through the nerves telling those blood vessels to shrink. The loss of blood volume makes the arteries, veins, and capillaries skinnier. Then the skin over them collapses into wrinkles.
Dermatologist Laurence Meyer of the University of Utah offers this explanation

The epidermis, or outer layer of the skin, is made up of cells called keratinocytes, which form a very strong intracellular skeleton made up of a protein called keratin. So when hands are soaked in water, the keratin absorbs it and swells. The inside of the fingers, however, does not swell. As a result, there is relatively too much stratum corneum and it wrinkles, just like a gathered skirt. (The hair and nails, which contain different types of keratin, also absorb some water. This is why the nails get softer after bathing or doing the dishes.)
Mark Changizi and his colleagues found evidence about wrinkled fingers and toes
Changizi and his colleagues found evidence that wrinkled fingers indeed act like rain treads, channeling water away from the fingers and toes during wet conditions, allowing primates – humans and macaques, to be specific – to maintain tighter grips. Changizi and his team analyzed photos of 28 human fingers.
Neurobiologist Mark Changizi of 2AI Lab thinks it’s got to be an adaptation. Consider tire treads. In dry conditions, smooth tires can best maintain their grip on the asphalt, which explains why race cars typically have smooth,
featureless tires. But when driving in rain, treads are far safer. Wrinkled fingers, then, could be optimally designed for grip in both wet and dry conditions.