This system is also known as a ducted warm-air or forced warm-air distribution system.
Schedule a professional tune-up every fall (before you first turn on your heating system). They will be able to test your heat exchanger for cracks, clean your pilot light, inspect the ventilation system, and much more.
When the thermostat sends its signal to the furnace, the furnace gas valve opens and ignites the burner component beneath the combustion chamber. The gas valve works with the thermostat to regulate the amount of gas that flows into your furnace.
To be clear, you may have a different heating system, such as a boiler, heat pump, or active solar heating. If your heating system heats water and you have radiators, you have a boiler. A heat pump is basically an air conditioner that works in reverse. Keep in mind that many homes have a hybrid heating system, which combines the energy efficiency of heat pumps for mild weather with the powerful heating capacity of furnaces during more extreme temperatures.