Why do we feel chilly after swimming on a warm and windy day?

The process described here is evaporative cooling. Evaporation occurs when liquid water absorbs heat energy and becomes a gas called water vapor. This energy is called the heat of vaporization. Water molecules are held to other water molecules by hydrogen bonds and a great deal of energy must be absorbed to allow a phase change to occur from liquid to gas.
The water on a person's skin on a warm and windy day would gain heat energy from the sun. Some of the liquid water molecules would be transformed to gas. This process requires heat energy to be absorbed by the liquid water in order for it to become water vapor. Therefore, the person's body would cool off as the water evaporates from their skin. 
This is the process of evaporative cooling which helps to stabilize the body temperature of organisms on Earth. Evaporative cooling allows the temperatures of the oceans to remain fairly stable allowing life to exist.