As an object nears the speed of sound the air is constrained by its inability to get out of its own way because the pressure wave can't travel faster than the speed of sound. Well below the speed of sound, the air is not constrained and, the air flows in response to the pressure differences rather than compressing. When air is compressed below the speed of sound the air is constrained from flowing by some kind of a container. The atmosphere is contained in a gravity well created by the gravitational field of the earth. This gravity well container is open on top rather than being a closed container so it does not constrain the subsonic air from flowing rather than being compressed.

All material objects are compressible if the pressure is great enough. Neutron stars are material that is compressed so that the electrons are squeezed into protons, thus creating neutrons as atoms collapse under the extreme pressure. If the pressure is even higher, matter collapes even farther into a black hole disapearing from our ability to see waht is going on because even light can't escape the gravitational field. Fortunately, these extremely high pressures aren't close enough to affect our everyday life much.