In a liquid you have billions of molecules all flying around bumping into each other.
All this random motion is heat. The faster they are going the hotter the liquid.
Now they are not all going at the same speed at any instant some are faster, some are slower overall they have an *average* speed, an average energy.
Now because they are in a liquid there are some attractive forces between them, however from time to time a fast moving one at the surface breaks free of all the others and takes off into the atmosphere - it evaporates.
Lets say over an hour we lose the 10% most energetic, fastest moving molecules - what happens to the average energy of the remaining molecules - it does down right - we've just lost the fastest moving ones!
So the average energy of the remaining molecules drops, the liquid cools.
This is why you get more evaporation at higher temperatures, more molecules have enough energy to break free.
There is a common misconception that boiling point is the temperature at which a liquid becomes a gas.
It isn't that happens through evaporation. BP is the maximum temperature a liquid can be. putting more energy in simply increases the rate of evaporation.
Hope this helps