Water evaporates because those higher energy water molecules at the surface escape into the air. But at the same time, some of the escaped molecules, because of their random motion, have a chance of returning to the water.
Air movement above water surface tends to carry away the escaped water molecules, thus reducing the number of molecules that would return to the water. That is to say, the number of water molecules leaving the water now becomes more than if there is no air movement. The water thus is observed to evaporate at a faster pace.