A vehicles thermostat is a valve that opens with the heat of the engine coolant and then closes as the temperature decreases.
The thermostat has a spring on it that allows it to open and close and if the thermostat gets stuck closed then the engine will start overheating because it's not allowing enough coolant to flow through the engine to keep it cooled down enough.
If the coolant thermostat is stuck open then the engine will be just fine and will stay even cooler which won't harm it.
But your cars heater may not work properly.
When your thermostat goes bad it will usually get stuck closed and cause your engine to overheat so if you notice your cars temperature gauge going up into the red zone within 15 or 20 minutes of the engine running then your thermostat could be bad.
You might also notice coolant leaks around the thermostat housing due to the build up of pressure in the coolant system because of the stuck closed thermostat.