Plain English Meaning
The gap between two pressures. Whenever the air on one side is at a different pressure than the air on the other side, that gap is the pressure differential.
Full Definition
The difference in pressure between two points or two sides of a barrier. In the vertical speed indicator (VSI), it refers to the pressure difference between the air sealed inside the instrument case (which leaks out slowly through a calibrated orifice) and the current static pressure inside the diaphragm. This difference deflects the diaphragm and drives the VSI needle to indicate rate of climb or descent.
Context Anchor
Seen in explanations of how the vertical speed indicator senses climb and descent.
Derivation
Differential comes from the Latin differre, meaning to carry apart or set apart. So a pressure differential is simply pressures set apart from each other -- one compared against the other.