Pressure breath helps to improve gas exchange across the alveoli by increasing the pressure in the lungs. The pressure breath helps to combat the effects caused by decreasing atmospheric pressure as climbers gain altitude.
From that, my best guess is that alveoli are not as efficient at the lower atmospheric pressures. By increasing the pressure in the lungs during a pressure breath you are basically making it seem like you are at a lower elevation (higher atmospheric pressure). And as a result the alveoli function better. Any thoughts?