Because water doesn’t have to boil to evaporate.
Water can evaporate at any temperature. In ELI5 terms, think of a glass of water as a whole bunch of tiny molecules stuck together. When they heat up, they vibrate, and eventually vibrate enough to ‘unstick’ from each other until a single water molecule will break free of the surface and float away into the air.
So, boiling water is just adding a lot of heat to the water which will make those bonds break faster and more violently, so the water will evaporate faster.
This is also why blowing on water will help it evaporate faster, the air molecules collide with the water molecules, transfer their energy to them and help them break free.
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