The change of a substance from its liquid state to its gaseous state at any temperature below its boiling point is called evaporation. In a liquid, the molecules are in constant random motion. The speed of these molecules keep changing due to their collisions with other molecules. If molecules near the surface of the liquid gain sufficient energy, they escape and become vapour.
This is the process of evaporation. When the temperature of the liquid increases, the average kinetic energy of the molecules increases. This means that there will be a larger proportion of the molecules that have sufficient energy to escape from the surface. Hence, the rate of evaporation increases with increase in temperature.