At any temperature, liquid molecules and other liquid molecules collide with each other and move irregularly. They move at different speeds, and fast molecules have more energy (kinetic energy in internal energy). When this energy becomes large enough to overcome the attraction between liquid molecules, this molecule can be separated from the liquid matrix and become an independent molecule, that is, gas.
But for the liquid, all the high-energy molecules run away, and the rest are low-energy, so the average energy of liquid molecules will become smaller during gasification. This is why evaporation lowers the temperature and boiling requires heat absorption. Why not say "boiling will lower the temperature"? Because boiling is a large-scale evaporation phenomenon, how can it become large-scale without adding some heat?
It should be pointed out that the increase of molecular thermal motion can only make the collision between molecules more intense, but not make the gap between molecules bigger. If the gap becomes larger, it means that the density of liquid becomes smaller. In fact, when a liquid is vaporized, its density is constant.