Definition:
The pressure a gas would have if it alone occupied the space in which it is being measured.
For example: Air is 21% oxygen and therefore the partial pressure of oxygen in air at the surface is 0.21, meaning that it would occupy 0.21 of the space on the surface. As depth increases, pressure increases so that at 10 meters (33 feet) of sea water surface pressure is doubled and air pressure is also doubled. This means that while air still occupies 21% of the volume it is now twice as dense and it's partial pressure is now 0.42. The partial pressure of oxygen reaches 1.0 at approximately 37.6 meters (123 feet) and at this depth breathing air is the equivalent of breathing pure oxygen on the surface.