When you hear someone say that air is not compressable when talking about airplanes, they do not mean that air cannot be compressed. For subsonic airplanes (less than 400 mph or so) air flowing over the aircraft does not compress (its density does not change). Pressure and velocity change, but density remains constant. The air acts like water or any other incompressible fluid. As an aircraft speeds up to about Mach .7 or so air flowing over certain parts of the aircraft like the tops of the wings for instance (remember that lift is created when air flowing over the tops of the wing accelerates, this increases its velocity and reduces its pressure, just like in the venturi of a carburator) will start to exceed the speed of sound. When the local airflow exceeds the speed of sound, shockwaves form. Air infront of the shockwave is compressed, its density changes, and air behind the shockwave has a lower density. Airflow is often disturbed by the shockwave, which will tend to move aft along the top of the wing to the joint between the wing and the control surfaces (or the tail and the elevator) this is why you will hear of WWII fighters having jammed controls in high speed dives, their thick wings would cause the airflow over the top of the wing to exceed the speed of sound at a relatively low speed. Modern aircraft have swept wings that are very thin to avoid this, and aircraft that can exceed the speed of sound have other special design features to overcome these effects.