When you get out of water, there are still water molecules in the liquid state on your skin. Some of those water molecules have enough energy to actually break out of the liquid phase and become gas (vapours). This is what happens during evaporation. Once the molecules become vapours, they are removed and thus the average energy of the remaining molecules decreases. This kinetic energy is directly proportional to the temperature of the liquid, and this leads to the cooling effect that you feel.
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