Body loses heat in 2 main ways. Evaporation of sweat and direct contact with the air.
Air can only hold a finite amount of both water vapor from sweat, and heat absorbed from the body.
Moving air increases the amount of air that is in contact with the body, think of it like if your body was handing boxes(boxes) to people in a line(air). It hands them one box, and it takes them a little bit to move out of the way for another person to get another box.
Moving air is like moving the line along faster, it can disperse more heat since there is more air. Your body interprets this feeling of loss of heat as feeling cool.
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