Air conditioning, as we know it, is accomplished by removing heat from the air and then distributing that cooled air throughout the house/building.
It is not possible to create cold. Cold is simply the lack of heat. Therefore, air conditioning works by removing the heat from the air as it passes through the system.
The warm air enters the air handler, located either in a closet or the attic typically. The air handler contains the blower and the coil. The blower is what blows the air through the duct system. The coil is where the magic happens.
The coil gets cold due to refrigerant (Freon) that is constantly running through it. As the warm air passed across it, the heat is absorbed and transferred into the refrigerant. The refrigerant then flows to the outside unit and the heat is released outside.
Still want to know more? Refrigerant inherently changes temperature as it changes pressure. As the pressure increases, it rises in temperature and vise versa. The compressor pumps the refrigerant into a high pressure and sends it through the coil in the condenser (the outdoor unit). The fan pulls air through that coil and the air removes much of that heat. The refrigerant then flows through a copper line into the house and into the evaporator coil (the inside coil in the air handler). The rate of flow of refrigerant is controlled by a metering device: either an expansion valve or a piston. As the refrigerant enters the evaporator coil, it drops in pressure allowing the temperature to drop and causing the coil to get cold. As the air blows across the coil, it absorbs the heat and takes it back outside through another copper line where the compressor pumps it through the outside coil again. That cycle continues as long as the unit is running.