Your automobile engine circulates water through the radiator to cool itself down when it is running. The engine operates most efficiently between certain temperatures. Too cold and it wastes fuel, too hot and it can be damaged, sometimes permanently. The thermostat is there to keep the cooling water from circulating from the engine through the radiator until the water that surrounds the engine (sometimes called the cooling jacket) reaches a pre-determined temperature.
It is important not to run the engine for long periods with a bad thermostat (or with no thermostat), because this can cause overheating if it is stuck closed, and reduced gas mileage if it is stuck open. Also, if you need to change your thermostat, be sure to replace it with one that opens at the recommended temperature for the engine. If an engine is modified for racing, then a cooler thermostat is sometimes used to compensate for inadequate radiator sizing, since racing engines tend to run very hot.
Another side effect of a thermostat that is stuck open is that your car heater will take longer to warm up because the heater takes it's water from the engine, not from the radiator. So if the engine is cooling prematurely, then the water stays colder longer.
If having a good thermostat in your engine causes overheating consistently, then you have another issue. It could be a cracked cylinder head, a plugged radiator, or a bad water pump. Hope this helps.