Evaporative air coolers blow air across a damp surface, which causes the air to cool down as it absorbs moisture. The system works in much the same way evaporating sweat cools down the body. Depending on conditions, these coolers can reduce air temperature by more than 20 degrees.
According to Chris Landers for How Stuff Works, evaporative coolers work best when humidity levels are extremely low, allowing more water to be absorbed by the air passing through the unit. Humid air is already close to the point of saturation and cannot absorb much more moisture, so its temperature will drop by a much smaller amount. In addition, using an evaporative cooler in a humid climate can cause excessive condensation that can damage walls and furniture.