Transonic flight is flight in the range between the onset of compressibility effects (around Mach number, M, of 0.7) and the establishment of fully supersonic flight conditions (around Mach number of 1.4).
While the aircraft itself may be traveling less than the speed of sound, the air going around the aircraft exceeds the speed of sound at some locations on the aircraft. In the regions where the local airspeed is near or greater than the speed of sound, compressibility effects are emcountered and the air density may vary because of local shock waves, expansions, or flow choking.
The first powered aircraft to explore this regime were the high performance fighters of World War II. These aircraft seemed to encounter a sound barrier at which drag was increasing faster than thrust. There was speculation in the mid-1940s that manned flight was not possible at speeds faster than the speed of sound, even though the muzzle velocity of rifle bullets is supersonic. Of course, the flight of the X-1A in 1947 proved that people could fly faster than sound and, until the retirement of the Concorde, any person with enough money could fly supersonic. As mentioned above, even though modern airliners typically fly at about M = 0.85, the flow over the wings is transonic or supersonic. Drag increases dramatically as an aircraft approaches Mach 1, so airliners use high thrust gas turbine propulsion systems. The wings of airliners are typically swept in planform to reduce the transonic drag. For Mach numbers less than 2.0, the frictional heating of the airframe is low enough that light weight aluminum is used for the structure.