This is because of "forced evaporation".
Water molecules with sufficient high energy will escape into the air. This is evaporation. If these escaped water molecules remain above the water on your hand, they will have a chance to return onto the water on your hand because of cohesive force between water molecules.
A blowing wind helps to carry the escaped water molecules away from your wet hand so that they will not be able to go back onto your hand. Thus evaporation goes faster if there is a wind blowing, your hand will be dried more quickly