There are lots of distinct types of central heating and air conditioning systems. The best one for you depends on where your house is located i.e. what sort of weather conditions you get, the size of your house, and your personal requirements i.e. the size of your loved ones.
The idea behind any system is the same i.e. you wish to warm the house when it's cold and cool it if it's warm, click here to know more.
A gas forced-air system is most likely the most popular central heating system today. Essentially a furnace heats the air that is then blown through your house by a system of lovers. When you wish to cool the atmosphere i.e. in summer, the exact same system takes the air in your house and moves it via a cooling apparatus.
That's the most elementary explanation but there is really an awful lot more to those systems. Yes but they're not very efficient, are more prone to being drafty, and could lead to needlessly substantial bills.
You might have a standalone electrical system that's popular as it's cheap to install. But it's expensive to operate and you can't add air conditioning to the identical system so that's an added cost should you require cool air in the summer.
You might have a water-based system often known as Hydronic. A hot water system operates on the premise that water is heated and spread through your house through a system of radiators which then emit warmth to those rooms. Radiators are becoming smaller and more powerful than those in use in the 1960s but it's still not an incredibly effective system and can't be used for air conditioning.