The old solution is that wrinkling is simply the result of your fingers and toes absorbing water after a long period of being submerged. But there are problems with this!
First: why is it only our fingers and toes that get wrinkly? Second: why is this such an unusual trait among mammals (only humans and macaques get wrinkly)? Third: why, if this is a simple tale of osmosis, do our fingers and toes cease to wrinkle when nerves to them are cut?
The paper, which you can read here, suggests that wrinkled fingers actually provide drainage for water so as to ensure greater traction, just like tires on a car. By examining the soaked fingers of 28 subjects, the scientists discovered that each finger showed a similar pattern of wrinkles: as the New York Times puts it, “unconnected channels diverging away from one another as they got more distant from the fingertips.” That allows water to drain away more efficiently from the fingers as they are pressed against an object, giving more surface area and a firmer grip.