The Air Handler is one of two major portions of an air conditioner system. It is what accepts the incoming air, conditions it, (heating it or cooling it) and then delivers that conditioned air to just one room or to the whole house. In many cases you will find this portion either somewhere inside the house, in the attic (bad choice unless you have a hot roof), in a crawl space (really bad choice unless you live in a dry climate), in the garage (bad choice no matter what), or occasionally outside when it is part of a packaged unit.
