This is a question that is surprisingly far from obvious. If you’ve learned about tonicity, then you might guess that, since your blood fluid is full of solutes, osmotic pressure forces water through your skin, causing the skin’s surface area to expand and wrinkle your digits. However, your skin is not that permeable, and wrinkly fingers are not the result of osmosis. In fact, think about this: if wrinkly fingers were simply due to water rushing into your skin, why wouldn’t your whole body wrinkle in the bath?
Rather, your fingers wrinkle due to an involuntary nerve response to moisture that causes your finger’s blood vessels to constrict and the upper layers of skin to pucker. It is thought that the channels created by the ridges in your skin help to channel away water. This is evolutionary adaptive because it allows you to grip objects more effectively when you are wet. Perhaps if I had written this is the bathtub, I would have been able to “grasp” a halfway decent closing joke.