Your central air conditioning system consists of two main parts - an outdoor unit and an indoor unit. An air handler is an indoor unit whose job is to effectively circulate conditioned air throughout your home. When matched with a heat pump, it circulates both cool and hot air, depending on the season. Air handlers are primarily used for these two situations:
1) In an area where heating is required yet gas is not available to power a gas furnace, and air handler can be paired with a heat pump. The air handler circulates the warm air from the heat pump through the duct system in the home.
2) Environments with year round warm weather do not need a furnace or heat pump, but will still use an air handler with an air conditioning unit as the air handler will move the cool air throughout the home, making for a more efficient operation as opposed to an AC unit working alone. That's because the more efficient your air handler is, the less work your outdoor unit has to do to make your home comfortable.