Temperature is a measure of average kinetic energy. To cause a phase change from solid to liquid to gas, add energy (heat). To change from a gas to liquid to solid take away energy (cool). Adding energy causes the water molecules to move faster. As a solid, molecules are moving very slowly and lock together in a hexagonal crystal and expand due to molecular attraction. As a liquid the molecules move faster and break free from the crystal structure but not from each other, like a piece of string. As a vapor molecules move fast enough to break free from the molecular attraction.
Airflow directs the energy to the wet materials and multiplies the effects of vapor pressure differentials. As evaporation takes place a boundary layer of high humidity hangs directly over the wet material, slowing or stopping evaporation, airflow removes this boundary layer. Rapid airflow also reduces pressure directly over the wet material causing the higher vapor pressure of the wet material to go to the lower pressure of the air. This will continue until the vapor pressure of the air equalizes with the vapor pressure of the wet material, then net evaporation stops. By adding energy (heat) to the air more water vapor will stay suspended it the air. That is why relative humidity is relative to temperature and expressed as a percentage of saturation at that temperature.
Humidity determines how much energy will be needed to allow a phase change. The lower the vapor pressure of the air the greater the differential is between the vapor pressure of the wet material you want to remove moisture from and the air where you want the moisture to go, the faster you will evaporate moisture. That is why it is necessary to dehumidify the air by venting wet air and bringing in dryer air or using dehumidifiers.