What is the purpose of the fins on the indoor and outdoor coils?

The fins act to distribute heat from the system or absorb heat into the system from the surrounding air depending on the location and purpose of the coils carrying the coolant. In a heat pump system, the fins function depends on which way the heat is being transferred. For an air conditioner, the indoor fins bring heat to the coolant from the air and expel heat at the outdoor fins into the air