In addition to the fan moving air away from you (the windchill effect, basically), your sweat also helps cool you off.
Substances have something called the latent heat of vaporization, which is a fancy phrase for how much energy you have to take away from a certain amount of substance (like sweat) to turn it into a gas.
In order for the sweat to evaporate, it uses energy from your body. More sweat evaporates when you blow more air at the human, causing more cooling.
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