The basics a homeowner should know about his heating and air conditioning system are that all systems have a way to heat or cool the air, a system to distribute the conditioned air and a method to control the heating or cooling. In the United States, most systems are forced air systems and use a system of ducts and blowers to distribute the heating or cooling to the home. They use a thermostat for control.
Most central air conditioners are split systems. They have a condenser outside the home and a set of evaporator coils inside the home. As warm air from the return duct blows over the evaporator coils, the refrigerant absorbs heat and converts the refrigerant to a gas. It travels to the compressor where it releases the heat as the device converts it into a liquid.
A heat pump works like an air conditioner in reverse. It takes heat from the outside air to warm the refrigerant so it becomes a gas and releases the heat in the coils in the air handler to warm the home.
Furnaces produce heat by consuming fuel. Those that use natural gas, propane or heating oil combine that fuel with oxygen in a heat exchanger where it burns to produce heat. Electric furnaces use electric resistance to produce heat.