It helps to think of a picture of dynamic exchange, where water molecules are continuously escaping cloth, whereas water molecules in air are hitting and going into the cloth. When the air has low humidity, the number of water molecules escaping is far higher than the ones that get into the cloth.
When exposed to sunlight or for that matter to an incandescent bulb in a room, the water molecules in cloth absorb energy, become more energetic and more number of them start to escape. So the cloth dries (remember water molecules in air continue to get into the cloth, but the number of molecules escaping has increased dramatically, so net effect is faster drying of cloth).
What wind does is sweep away those water molecules that have escaped the cloth and reduce the concentration of water molecules in the cloth vicinity, thereby reducing the rate of water molecules getting back into cloth. This results in faster cooling)