Plain English Meaning

Air pushes on every part of a wing, but if you added all those pushes together you could replace them with one push at one spot. That spot is the center of pressure. It doesn't stay still — it slides forward and backward along the wing as the wing's angle to the airflow changes.

Full Definition

The center of pressure is the single point on a wing (or other airfoil) where the total aerodynamic force from the airflow can be considered to act. Lift and drag are produced unevenly across the whole wing surface, but their combined effect can be summed up as one force acting at this one point. The location of the center of pressure shifts along the chord of the wing as the angle of attack changes — generally moving forward as angle of attack increases, and rearward as it decreases.