The perspiration on your body evaporates and cools your body. Water kept in a porous container is cooled on a hot day. The water seeps from the inside. There is a small amount of water on the outside surface. The surface water is vaporized—it evaporates.
Much of the heat required for vaporization comes from the liquid in the container. When heat is removed this way the liquid is cooled. The heat is carried away with the vapor.