Differential air pressure is a term of comparison. It may be stated as "the difference in air pressure between..." and finished from there. Let's look at a sentence and then break it down.
"The differential air pressure across the body of the 747 is a cause of concern over the life of the aircraft."
A jet at altitude has a pressurized cabin. The outside air pressure is very low. (Think Mount Everest. Almost no one climbs it without suplimental oxygen.) There is a difference between the air pressure inside the cabin and the air pressure outside the cabin. This is an instance of differential air pressure. The differential air pressure puts stress on the body of the plane. When the aircraft is back on the ground, the differential pressure disappears. The alternating application and neutralization of stress across the hull damages the structure over the life of the airframe. The differential pressure is the difference between the pressure of the air in the (pressurized) cabin at altitude and the pressure of outside air at that altitude.