Here is a simple illustration of what happens when evaporation occurs: If you make the back of your hand wet with some water and blow air across it to make the water evaporate, does your hand become warmer or cooler? It becomes cooler. The reason for this temperature change felt on your skin is that some of the water molecules that left the liquid state to become a single gaseous molecule took some of the thermal energy from your skin to keep it jiggling fast enough to break their bonds with the other water molecules in the liquid state. This is called evaporative cooling. This principle of a thermal energy being lost [or colder] from the liquid or the material upon which it is in contact when evaporation occurs is one mechanism that may be used to evaluate the rate of net evaporation –or for that matter, the quantity of humidity within the mixture of gasses that comprises the air sample.
The difference in temperature of a dry thermometer and the temperature of a wet thermometer (that is evaporating its moisture) can be used to measure the quantity of humidity in this air Mixture.