Plain English Meaning
Air can be squeezed. At low speeds this is so small it’s ignored, but as an aircraft gets close to the speed of sound, the air in front of it bunches up instead of flowing smoothly aside. This changes how the wings and controls behave.
Full Definition
Compressibility is the property of air by which its density increases when it is subjected to pressure. As an aircraft approaches the speed of sound, the air ahead of it can no longer move out of the way smoothly and begins to pile up and compress, causing sharp changes in pressure, density, and local airflow speed that significantly alter lift, drag, and control behavior.
Context Anchor
Seen in discussions of high-speed flight, , and the between and airflow.