Cooling fans work in basically two ways. One, they are often used to move air around within the house making occupants feel cooler. In this mode of operation, they do not actually cool the air. In fact, a fan operating in a "closed" room will increase air temperature, because of electrical losses from the motor. However, they make occupants feel cooler by moving air across their skin. The moving air causes moisture on the skin to evaporate taking heat with it. The cooling effect of moving air is directly related to the speed of the air, which increases the body's evaporative cooling. You have probably heard about "wind chill" in winter making it feel colder outside than it really is. Fans are accomplishing the same effect in your home by increasing the wind speed across your skin.
The second way fans are used to cool is by moving hot "inside" air out of the home, so it can be replaced with cooler "outside" air. In this use, fans make you feel cooler because the air really is cooler where the first cooling method, the air is getting warmer from using the fan to cool the body.
Compared to refrigeration units, fans are much less expensive to purchase and use very little energy. For these reasons, most homes in this country use of some form of fan cooling. Even homes that use air-conditioning during the hottest months of the year, usually use fans to reduce the amount of time (or number of months) the air conditioner must operate. Systems that rely on the movement of air include: natural ventilation through "open" windows, window fans, portable fans, ceiling fans, whole-house fans, attic vents, and passive ventilation.