The potentiometer controls the gate voltage to the Thyristor or more likely a triac.
The timing of the gate voltage controls the amount of ac waveform that flows through the input to output.
So when the potentiometer set at maximum output, the waveform is a full ac cycle and at minimum level the ac waveform is chopped down to a pulse. This changes the power output since only a part of the waveform gets through.
note: A Thyristor only allows the positive half cycle through the device and a Triac allows the full ac waveform through.
So don't use the potentiometer on its own otherwise it will have to carry the full current of the load and is likely to burn out. There are devices you could use but these will need to be rated for the load and are likely to generate heat, which is not what you want in the back of your switch plate.
