An increase in atmospheric pressure raises the boiling point of a liquid by raising the vapor pressure of the water above the liquid. This increases the amount of thermal energy needed to increase the vapor pressure of the water to match, raising the boiling point. Conversely, a reduction in atmospheric pressure, such as that caused by an increase in altitude, lowers the boiling point proportionately.
The vapor pressure of a liquid determines how quickly molecules leave the liquid state and convert to gas. Under normal circumstances, the vapor pressure of water is low, resulting in few molecules leaving the liquid via evaporation. Heating the liquid increases the kinetic energy of the molecules and also increases the vapor pressure of the liquid. Once the vapor pressure equals or surpasses the vapor pressure of the outside atmosphere, the water converts to gas rapidly.
Pressure cookers take advantage of this phenomena. Normally, boiling water cannot cook food to more than 212 degrees Fahrenheit, as that is the boiling point of water under one atmosphere. By raising the pressure inside the vessel, however, a pressure cooker increases that temperature, allowing food to cook much faster.
High-altitude cooking and baking recipes take into account the lowered pressure and lowered boiling points at elevation and adjust cooking times accordingly.