An evaporator coil is a series of piping contained inside a metal cabinet that sits on top of a furnace. The evaporator coil has piping that runs outside to the air conditioner as well.
When cooling in the summer, an air conditioner sends chilled refrigerant (such as modern R-410A) inside to the evaporator coil. The furnace fan pulls air from the home via the return air ducts, and forces this air through the frigid evaporator coil piping. The coil extracts heat from the air while moisture also condenses on the cold piping, removing extra humidity.