Why does evaporation causes cooling?

Evaporation of a liquid from a surface causes a cooling effect.
Evaporation involves the phase change of the substance from the liquid to a gaseous phase. An example is that of the liquid water converting to water vapors. Also, note that the molecules in the gaseous phase have higher kinetic energy as compared to the molecules in the liquid phase.
For the phase change, the molecules of the substance (in the liquid phase) must gain additional energy to raise their kinetic energy levels. This energy is obtained in the form of heat from the surroundings. Once the phase changes, the substance evaporates accompanied by a reduction in the heat levels of the surroundings. This is what causes the cooling effect.
The most common example is the cooling effect generated by perspiration from our body. Note that evaporation of some liquids may result in a better cooling effect than that of water. Evaporation of alcohol (say, rubbing alcohol or isopropanol) has a faster cooling effect because of the volatile nature of the alcohols.
Hope this helps.