At the most basic level, a thermostat is a device that controls the temperature in your home. Not only does it tell you what temperature your home is, it allows you to adjust it using a digital interface or a dial. Depending on the sophistication of the thermostat, it may allow you to control when and by how much the temperature rises, even if you are not in the house. Similarly, some new models of thermostat work entirely wirelessly, and you can do the programming from your smartphone via a specially designed app.
Another thing to consider is that the more control you have over your home thermostat, the more money you will save. You will not risk heating or cooling an empty house, and you can decide how much power you want to use.