[basjoos]

There are two mechanisms involved in improving your mileage when the humidity is high. In humid air, water molecules (which have a much lower mass than nitrogen, oxygen, or carbon dioxide molecules) displace some of the N, O, and CO2 in the atmospheric mix, which reduces the total tonnage of gas molecules that your car is shoving aside as you drive down the road (reduced aero drag).

Secondly, the extra water molecules also reduce the amount of oxygen available in the intake air feeding your engine, so the engine controller reduces the amount of fuel injected to maintain the proper stoch ratio, which (derates) reduces the maximum engine power available. This reduced power output also forces you to maintain wider throttle (for reduced pumping losses) to produce the same power output that you would get with low humidity air.

These two factors; reduced aero drag and reduced engine power is also why you get better mileage in the thinner air at higher elevations, something aircraft pilots have been taking advantage of since the dawn of aviation.

The reduced oxygen level in humid air is also why people with reduced lung capacity sometimes have problems breathing when the humidity is high.

You get your best mileage under hot, humid conditions and at higher altitudes, i.e. lower air densities, and the worst mileage under cold temps, low humidity, and at lower elevations, i.e. higher air densities.