A body moving through the air pushes the air aside. Small disturbances move away at the speed of sound. Disturbances from a slowly moving body go out in circles, like ripples from a pebble in a pond. If the body moves faster, the circles are closer in the direction of travel. If the body is supersonic, then the circles overlap. The envelope of circles forms a cone. The angle of the cone is determined by its vertex moving in the body's travel direction at the body's speed, while the circles grow at the sound speed.
(from Aircraft Noise by Michael T Smith, Cambridge, 1989) " .. When the speed of an aircraft is supersonic, the pressure waves cannot get away ahead of the aircraft as their natural speed is slower than that of the aircraft. Slower, in this context, means just over 1200 km/hr at sea level and about 10% less at normal cruising altitude. Because they cannot get away, the pressure disturbances coalesce and lag behind the aeroplane, which is in effect travelling at the apex of a conical shock wave. The main shock wave is generated by the extreme nose of the aeroplane, but ancillary shocks are generated by all the major fuselage discontinuities. .. "
The existence of the "Mach cone", "Mach waves" and the corresponding angle, was discovered by Ernst Mach in the nineteenth century.