The heater matrix is a small heat exchanger positioned by the engines cooling system. Hot water passes through the heater matrix and air passing over it is therefore heated. Depending on how your set the controls you can either direct the hot air towards you in the car, away from you or mix hot and cold to get the temperature you require.
When the heater is turned on by the driver, a diverter door opens to the heater core area in the dashboard. A small fan (commonly referred to as a heater/blower motor) blows air across the hot heater core into the duct work of the dashboard and into the interior of your car. When the heater core leaks (it leaks anti-freeze) it will usually leak inside the car on the passenger floorboard under the carpet. If your heater isn't working properly, or if you smell a sweet odour, investigate the passenger side floorboard for signs of anti-freeze leakage. A leaking heater core may also cause a greasy film on the inside of the windows.
A heater matrix does not normally malfunction but they can get blocked. High quality

heater matrices

for any car can be bought should yours get damaged or become blocked, preventing you getting any hot air.