The term for a liquid turning into a gas at its surface below its boiling point is evaporation.
Evaporation is a surface form of vaporization. Molecules in a liquid are constantly moving with a range of kinetic energies; some molecules at the surface have enough energy to overcome attractions from neighboring molecules and escape into the surrounding air as vapor. This can happen even when the liquid is far below its boiling point.
Temperature, exposed surface area, airflow, and humidity all affect the rate. A warmer liquid has more high-energy molecules, a wide puddle exposes more surface, moving air carries vapor away, and dry air allows more water vapor to enter it. Evaporation also removes higher-energy molecules, which is why perspiration cools skin.
Evaporation differs from boiling. Boiling occurs throughout the liquid when its vapor pressure matches the surrounding pressure, producing vapor bubbles. Condensation is the reverse process, in which gas becomes liquid. Sublimation is different again: it is a direct change between solid and gas without a liquid stage.