Temperature, as you may know, is basically a measure of kinetic energy of the water molecules. These molecules will constantly collide and thus exchange some of that impulse.
That’s wy, at any temperature in any medium, there is a distribution of different velocities and some of those will be fast enough to change state. When these are near a water surface, they can leave the water and turn into steam, so to speak.
This happens all the time and also the other way around, which is why evaporation is faster in dry air.
Boiling is just the point, at which steam bubbles will spontaneously form, which is a whole different can of worms.
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