In a nut shell, a TRV works by adjusting the temperature of a radiator in accordance to the temperature of a room. It does this by adjusting the flow of hot water into the radiator. As the room cools for example the valve recognises this and allows an increased flow of hot water in to the radiator. When the room is heated to the desired level the valve will work to maintain the temperature by gradually closing the valve to decrease the heat in the room and the rad.
To work effectively TRV's need a free flow of air around them so they can sense the room temperature. If they are smothered by curtains or furniture it will hamper their performance in heating the room.
The following points should be noted:
TRV's do not a directly control the temperature of the boiler, this is controlled by the room thermostat.
By turning the TRV's up, this doesn't mean the room will heat up any quicker, only that the room will be regulated at a higher temperature. The speed of how quick the room warms is due to the size of the boiler and the material choice and surface area of the radiators in the room.
For a more detailed explanation of how thermostatic valves work please watch the video below.