Why should we cover a frying pan with plate while cooking or use pressure cooker? Will it save cooking gas?
Water in the food your trying to cook has a certain boiling point. This boiling point is elevated with increase in pressure (since under high pressure, vapors tend to condense back). To cook the food properly, you'd want the water to stay as liquid as much as possible, even under high temperatures, due to the fact that liquid water has a high specific heat capacity, storing lots of heat energy for a given temperature and can transmit heat to food better. Under pressure, boiling point of water is increased, so that it still remains liquid. This helps cook the food faster than without pressure.
I think that you are talking about pressurized pots.
If this is the case I think looking at the ideal gas equation will give us a hint on what happens. $$pV = nRT$$ Where $p$ is the pressure of the gas, $V$ is the volume of the gas, $n$ is the number of moles of the gas, and $R$ is the gas constant.
In the pressurized pot the volume is assumed to be constant, and this is a valid assumption as the amount of water that is vaporized is small and could be neglected in order to get a more qualitative result, if however we want a more detailed result, then we wouldn't neglect any thing and we would use a real gas equation.
As we increase the temperature, the number of moles of the vapor increases and they both increase the pressure of the water vapor. The increased pressure is the key for the result that we will get shortly.
If we looked at the phase diagram (specifically at the liquid phase) we see that as we see that as we increase the pressure the boiling point of water (or liquid) increases and this allows to get to higher temperatures that is not achievable within normal pressure.
In short, heating pressure pot increases the pressure above the water which increases the boiling point of water and allows reaching of higher temperatures which speeds up cooking.