Before you understand what a sonic boom is, it is important to understand what a shock wave is since these are closely related.
We start though by showing you the differences between a bow wave and a shock wave. This will help you quickly understand what a shock wave is.
Having said that, what is a sonic boom? Air usually gets out of the way of an aircraft when the speed of the aircraft is less than that of sound. However, when an aircraft is traveling at a speed greater than that of sound, air cannot get out of the way fast enough. This will cause a sudden increase in air pressure behind the aircraft. This air pressure looks like a three-dimensional shock wave as shown below.
When the shock wave reaches the ground, people near by the wave will hear a sudden explosive noise. This noise is called a sonic boom. In the figure above, the guy on the right has already heard the sonic boom. However, the guy on the left will hear it shortly.
Notice that the overlapping spheres will indeed create a cone. May be you wondering at this point why the wave is made by spheres instead of circle.
To see a real life example of what a sonic boom is , I encourage you to check this video. You will see the cone shape behind the aircraft after it passed the speed of sound.
Don't confuse the sound that you hear with the sound that an object may produce as it moves such as the sound coming from an engine. If superman could throw a rock at a speed greater than that of sound, you will hear the sonic boom as the rock is passing by you.
When a lion tamer cracks a whip, the tip of the whip will travel faster than the speed of sound. As a result, you hear a sonic boom as well.
In summary, when a plane is traveling faster than the speed of light, a shock wave will form behind the airplane. The shockwave creates a sonic boom. However, to hear the sonic boom, the shock wave has to reach your ear.
Hopefully by now, you clearly understand what a sonic boom is.