Temperature is a description of the average molecular kinetic energy of a substance (water in this case).
The “average” aspect is very important in this case because not all of the molecules are moving with the same speed. Some are faster, some are slower.
The faster molecules are usually prevented from escaping the rest of the water because they bump into other molecules along the way, transfering their energy. However, occassionally, a molecule gets enough velocity and is close enough to the surface to escape the rest of the water and become a molecule of water vapor. That molecule has a higher portion of the energy of the total volume of the water, and takes that energy with it, resulting in the average energy (and thus temperature) of the water falling.
Now, one molecule isn’t going to take a whole lot of energy with it, but there are a *lot* of molecules of water in a drop of water, so you have millions of molecules escaping this way and taking their energy with them, resulting in a noticable drop in the temperature of the remaining liquid water.
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