This article relates to vehicles with water-cooled engines and doesn't apply if you drive an old Volkswagen with an air-cooled engine or a new electric car.
Most cars on the road have water-cooled engines, and their heating systems work on the same basic principle. Hot coolant from the engine passes through a heater core, which looks and functions like a small radiator, and a blower motor forces air through it. The coolant then heats the air, and the air, in turn, warms the interior of the vehicle.
This is the reason that it takes a while for heaters to start blowing warm air. Until the engine warms up, there's no heat for the heater core to extract. It's also the reason that a plugged heater core, stuck thermostat, or air in the cooling system can cause a car's heater to blow cold.