What does the heater core do?
The heater core is located under the passenger-side dash up in the footwell. It's behind that whole mass of black stuff you see up there looking in behind where your glovebox is located.
The heater core is like the radiator, except that the air that goes through it is the inside air for your car. The hot coolant, which comes through the small hose on the water pump, flows through it and provides the heat, then flows back into the engine via a connection at the rear of the passenger side cylinder head.
The air speed/volume of the air blowing through the heater core is controlled by your blower motor. There is a flap in the heater assembly that decides how much air goes through the heater core and how much bypasses it (that's controlled by your temperature selection lever). So if you want hot heat and a lot of it, you slide your temp selector to hot and turn up the blower to max.
Because of the *obscure* location of these items (heater core, blower motor), replacing them is a major PITA. You're read what has to happen to get at the heater core -- for the blower motor you either have to drop the passenger side fenderwell to get it out of the way, or cut a hole in it to get at the motor. A lot of people opt for that -- Barbara (2boxerdogs on TAC) found that when they started restoring their TATA, so they had to weld in a new patch panel to replace the crude patch they found when they tore it down.
It's really surprising that heater cores don't go bad more often, considering they are really just like the radiator and are full of coolant all the time.