Your body, as a warm-blooded animal, tries to keep a constant temperature (around 98°F or 37°C). Thing is, the body is constantly producing more heat (your metabolism at work…) and needs to get rid of the excess. If the air around you is at the same temperature as you are, it is very hard for heat exchange to take place (for you to get cooler as the air gets hotter) and, thus, you overheat a bit and feel warm.

This is why wind makes you feel cooler: it moves the heated air away from your body and brings in new, cooler air, making the exchange more efficient. Evaporation takes heat away as well, hence we sweat to col ourselves down.