The fins and coils in an electric baseboard heater, often made of conductive materials like copper, play a critical role in its heating capabilities. The heating element warms up the coils, which in turn heats the fins. The fins increase the surface area of the heater, allowing for more efficient heat transfer to the air. Cooler air at floor level is drawn into the bottom of the unit, heated by the coils and fins, and then released from the top of the unit as warm air, creating a flow of warm air in the room.