The speed of sound is the speed at which sound vibrations move through a medium. In air at sea level, this speed is about 340.29 m/s (761 mph or 1,225 km/h). The speed of sound varies with the temperature of the air, but is almost completely independent of the density. Breaking the sound barrier was a major goal of aviation for its first 50 or so years, until it was eventually achieved on 14 October 1947 by airman Chuck Yeager flying in a Bell XS-1, now on display at the National Air and Space Museum.
The first self-propelled object to break the sound barrier were German V-2 missiles launched during WWII. By 1944, these missiles regularly traveled at four times the speed of sound (Mach 4) during descent. When missiles, airplanes, or any other fast object is breaking the sound barrier, it causes a sonic boom, a loud boom caused by colliding pressure waves around the object. Thus, when these missiles were launched en masse, the air was filled with the noise of sonic booms.
As an object travels through the air, it gets surrounded by spheres of pressure, caused by the displacement it creates in the air due to its movement. As an object moves faster and faster, it starts to catch up with these pressure spheres in one direction, causing them to be compressed ahead of the craft. A measurement would find that the air is much denser than typical air, while the air behind the craft is thinner. When the craft is breaking the sound barrier -- moving faster than about 761 mph -- the air in front compresses so hard that the pressure spheres begin to get left behind the plane. They can't expand out in front of the plane faster than they are being generated.
In the old days, breaking the sound barrier was a big deal -- it led to a loss of control in flight and major vibrations. Modern aircraft, which include features like swept wings, optimal fuselage shape, and stronger engines, can make it through the sound barrier without much trouble at all. Most of the time, it isn't even noticeable. Breaking the sound barrier is usually something for military aircraft, as few commercial aircraft have top speeds over the speed of sound.
In the late 1950s, many aircraft companies thought that supersonic aircraft would be the next logical step in air travel, leading to the development of craft such as the Concorde and the Tupolev Tu-144, which entered service in the 1970s. Some futurists expect supersonic aircraft to make a comeback in the late 2010s.