A dehumidifier is an appliance that reduces the humidity in a room by condensing moisture in the air on to a cold surface. A dehumidifier works in a similar way to an air conditioner, the main difference being that it has both its hot and cold coils in the same box.
Air is drawn in by a fan and moisture from the air condenses on one set of coils much like an air conditioner's evaporator coils. The water drips into a removable bucket or through a hose to a drain. The other coil warms the air, which is blown back into the room.
Although a dehumidifier doesn't cool the air in a room (in fact it heats it slightly), it makes it more comfortable because it decreases the humidity. Most dehumidifiers don't work well under about 65°F because at these temperatures the cooling coil would have to operate below freezing point to condense any moisture.
See also humidity reduction in the home.