An air conditioner's main job is to cool the air, but it also controls humidity and it filters, cleans and recirculates air within a house. If the unit is too small, it won't provide sufficient cooling; if it's too large, it will cool quickly and shut off before removing a sufficient amount of moisture from the air.
An evaporative unit (called a "swamp cooler") is typically used in dry desert regions. These units are mounted on the roof or beside the house. Inside the unit, water is sprayed on a sponge-like blanket and hot outside air is pulled through the blanket by a blower, causing the water to evaporate and cool the air. The cool air enters the house, forcing hot stale air through open windows.
A refrigerated system simply absorbs heat from air within the house and transfers it to the outside. The system contains a liquid refrigerant that is turned into a gas which flows through evaporator coils, cooling the coils and extracting heat and moisture from the room air. Then, the warm gas flows into the compressor and it is heated by compression. The hot gas enters the condenser where the coils dissipate heat to the outside. A condenser tray catches the moisture and discharges it to a waste drain or directly outside.
An integral system has all components encased in a single unit. It can be located in the attic or crawl space, with ducts through the exterior wall to provide air for cooling the condenser. In a split system, the compressor-condenser is located outside and the evaporator coils are located in the house.