A sonic boom is the loud, ear-splitting noise created by a shock wave from a supersonic plane (a plane travelling faster than the speed of sound). As a plane flies, it pushes sound waves out in all directions. A plane travelling faster than the speed of sound passes the sound waves it has already made. The overlap of waves builds up pressure and creates a shock wave. The shock wave follows the plane like a boat's wake. People on the ground hear a noise like thunder as the shock wave rolls by.
In this photo, taken using a special imaging process, you can see shock waves created by an aircraft travelling faster than the speed of sound. The white streak behind the plane is the engine exhaust.