A thermostatic radiator valve is a very simple device which has a very big role in energy saving. It is basically a local area thermostat designed to aid in keeping the area around the TRV at your desired temperature set on the TRV head. So in essence it is aiding the room temperature keeping it consistent and not getting to hot and wasting energy, as well as making the room easier to control to your personal comfort temperature for that room.
Most homes have a single thermostat on the wall of one room, and the fairly inaccurately determined set-temperature of that room switches off the heating for the whole home when it is exceeded. That can easily still have heat being pumped out of the radiator in another room when the sun or cooking or some other appliance is heating it too. Thermostatic valves individually switch off each radiator to which they are fitted when the desired temperature has been reached in its vicinity
The workings are very simply which makes them highly reliable. One thing to be cautious of is trying to keep the area around the TRV free to allow for air movement so the TRV is as accurate to the room temperature as possible. For example, if there is a long curtain draped over the TRV there will be no air circulating around the valve and behind the curtain will get stuffy and the TRV will react accordingly reducing the radiator heat out-put even though the room may not be at the desired temperature.