Evaporation is one of the four principal ways that heat can be transferred (the other three are radiation, convection, and conduction). Evaporation of sweat from the skin is an endothermic reaction: the reaction essentially "consumes" heat, which cools the body in the process.
For a liquid to turn into gas, either by boiling or evaporation, energy is required. This is known as the latent heat of vapourisation. In the case of boiling this is provided by external heat sources but in the case of evaporation it has to come from within the liquid itself, thus cooling it.
The energy is required to break the strong bonds between the molecules in the liquid and allow them to break free in gaseous form.
Evaporation is an endothermic (heat-absorbing) process because molecules must be supplied with energy to overcome the intermolecular forces.
Evaporation occurs at the surface of a liquid, and energy is required to release the molecules from the liquid into the gas. The use of this energy, known as latent heat, causes the temperature of the liquid to fall.