What exactly is a hot air pressure regulating valve, and what is its purpose?
The hot air pressure regulating valve does not generate hot air. The hot air is generated from the engine bleed air. 

But that air does not go straight from the engines into the cabin, it would be too hot. If you want to adjust the temperature, you need a way of limiting the amount of hot air going into the cabin. That is what the regulating valve does (in conjunction with a couple of other components).