Air conditioning systems work by moving heat from inside your premises to the outside. In a central AC system, air is drawn into the ductwork system through the return air system. Installed in the return air ductwork is an evaporator coil. This coil is connected to the condenser, the unit that is outside your building, by copper tubing. The refrigerant is then pumped from the condenser to the evaporator coil. As the refrigerant passes through the inside of the evaporator coil, warm air from inside your building passes over the outside of the coil. Because the refrigerant is cooler than the warm air, the refrigerant absorbs heat from the air. The refrigerant is then sent outside to the condenser unit. When the warmed refrigerant is in the condenser unit it is compressed by the compressor; the compression of the refrigerant causes it to boil. As the refrigerant boils it gives off the heat it picked up from inside your premises. The refrigerant is then passed through the coil in the condenser unit where it gets cooled again and is ready to go back inside to pick up more heat from your premises.
As this whole process is going on, the temperature and relative humidity in your premises are both lowered. The relative humidity level drops because cooler air cannot hold as much moisture. As the air cools, it gives up some moisture and it gets collected in the base of the evaporator coil and is then drained away.