I like to explain the physics this way: heat is a thing, temperature is a place. If you put a hot thing next to a cold thing, heat stuff will flow out of the hot thing into the cold thing. This will cause the cold thing's temperature to rise, and the hot things's temperature to fall, unless other factors interfere. How far and how fast these temperatures move depends on the material: dense things like iron can absorb a lot of heat but temperature rises slowly. Light things like air gain or lose temperature quickly as heat moves.
For a stove burner, you have continuous input of more heat, so the burner's temperature will not fall. The liquid in the pot is mostly water, which can absorb a lot of heat and its temperature will rise--to a point. What interferes is called a phase transition (what you and I call boiling). At this point, further heat energy going into the water is used to turn it into steam, while the remaining water stays in place (this place is about 100C at normal pressure).
Putting the water under pressure changes the place at which this transition happens, and so the water can absorb more heat, going to a higher temperature, before turning into steam.