Vapour pressure in an enclosed container with liquid at normal conditions
The kinetic theory of gases is based on the idea that particles are moving randomly. Even if all particles started motion with exactly the same speed, as they interact with each other and the walls of the container their velocities would become randomized. The kinetic energy of particles at a given temperature is an average; some particles are moving much faster, and can escape from a liquid. These faster-moving particles, removed from the liquid, leave the liquid a bit cooler. Thus, evaporation puts a liquid into a gas and chills the liquid.

For a more complete explanation, see this video.