A "thermostat" is a device which controls the temperature of a heater. A thermostat allows you to choose a certain temperature that you want a room to be. When it gets warmer than that temperature, the heater will turn off.
Most thermostats control the heat in a house, but some cars also have thermostats now as well. So do hot water kettles, swimming pool heaters, and other devices which need to maintain a constant temperature.