Air handlers and furnaces aren't typically installed in the same home in North America. If you have a furnace, you most likely won’t need to think about an air handler.
Air handlers are frequently paired with heat pumps and manage airflow across your residence. Some systems also provide extra heating and cooling pieces to support the heat pump.
A furnace heats in a different manner by pushing heated air into your vents, which send it across your residence. Since furnaces depend on combustion chambers to produce heated air, they don't have some of the parts you'll see in a standard air handler.