The concept is evaporative cooling. Essentially a liquid does work on the environment by expanding itself, thereby lowering its own internal energy.
This expansion is made possible by the fact the the liquid can convert itself into gas. The particles that manage to do this are on average possessing more KE than the other particles (remember that particle KE are not uniform but follow a Boltzmann distribution, and only particles with enough KE to break intermolecular bonds can become gas), in other words evaporation causes the remaining liquid to have on average, lower KE particles (a drop in temperature). Necessarily the particles that managed to escape are at the appropriate higher temperature, and as a result expand the volume they take up (do work) until back in thermal equilibrium with the liquid or environment or both. The result is both the liquid and it's vapor blanket being a lower temperature than before being exposed.
If there is zero convection of this vapor then net evaporation eventually stops (condensation of the vapor back into the gas liquid interface equals evaporation) and the cooling effect ceases. if the whole shebang is enclosed in fixed volume then temperature as well as pressure will increase (heat is from environment) until all the water and water vapor is at environment temperature. The gas pressure of this vapor is know as the vapor pressure, which is dependent on temperature.
In reality, convection is non zero. There are breezes, and warm vapor rises away on its own, creating more opportunity for the liquid to vaporize and continue losing energy by losing its fastest particles to the environment. Exposed water bodies are typically a few degrees below air temperature because of this.