You can learn a lot about sonic booms by looking at the wakes boats leave in the water.
If you toss a pebble in a pond, little waves will form in concentric circles and propagate away from the point of impact. If a boat travels through the pond at 3 to 5 miles per hour, little waves will propagate in the same way both ahead of and behind the boat, and the boat will travel through them.
If a boat travels faster than the waves can propagate through water, then the waves "can't get out of the way" of the boat fast enough, and they form a wake. A wake is a larger single wave. It is formed out of all the little waves that would have propagated ahead of the boat but could not.
When an airplane travels through the air, it produces sound waves. If the plane is traveling slower than the speed of sound (the speed of sound varies, but 700 mph is typical through air), then sound waves can propagate ahead of the plane. If the plane breaks the sound barrier and flies faster than the speed of sound, it produces a sonic boom when it flies past. The boom is the "wake" of the plane's sound waves. All of the sound waves that would have normally propagated ahead of the plane are combined together so at first you hear nothing, and then you hear the boom they create.
It is just like being on the shore of a smooth lake when a boat speeds past. There is no disturbance in the water as the boat comes by, but eventually a large wave from the wake rolls onto shore. When a plane flies past at supersonic speeds the exact same thing happens, but instead of the large wake wave, you get a sonic boom.
Here are some interesting links: