An AC condenser cools a substance from a gaseous to a liquid state, releasing the heat contained by that substance so it can be directed away from the area getting cooled.
There are many kinds of condensers, ranging in size from portable to industrial. Many use water or local air as the coolant, dripping the condensed liquid onto a collecting pan called a hotwell. Water based systems use a "jacket" for containment, and the simplest and cheapest kind of condenser (the "Liebig") is essentially a straight tube through which the cooling substance flows. More complicated condensers use more complex shapes, from twisting turning pipes to materials that have special properties on the micro-scale.
Most standard window AC units use air cooling methods, releasing liquid harmlessly to the outside of a home. These are easy to clean, and thus require little maintenance. Water cooling is more typical for larger systems, like swimming pools and urban plumbing. They're more efficient than air coolers, but require both more upfront investment and upkeep maintenance. Evaporative coolers are used in large systems where water is not readily available.
A typical central air conditioning system uses a fan to blow air from outside the machine through a heat exchanger, condensing vaporous refrigerant into a liquid, and a compressor to move this substance through the appliance by increasing its pressure.