Evaporation is liquid water moving into the air. It can happen long before water boils.
At the surface, some water molecules move fast enough to leave the liquid and enter the air as vapour.
Heat speeds things up, but it is not the only factor. Dry air, wind and a larger exposed surface can all increase evaporation.
A drying puddle, wet clothes and sweat cooling the skin all rely on the same process. Water vapour itself is invisible.
Evaporation depends strongly on conditions. A larger exposed surface, dry air and moving air all help molecules leave. That is why a spread-out towel dries faster than a crumpled one.
A useful way to understand this phenomenon is to separate the driving force from the visible result. Temperature, pressure, concentration, surface area and the nature of the materials can each change the rate or the final state. In real systems, several of these factors often act at the same time.
That is why the same phenomenon can look different in a laboratory, in the kitchen or outdoors. The underlying chemistry or physics stays the same, but the conditions change the balance.