I explain it to my students in terms of Sonic Booms.
Stripped down to absolute basics here, there are two velocities relevant to the reception of waves:
The velocity of the source - so if you here a siren, it's the firetruck/ambulance/etc that is the source.
 2. The velocity of the wave/medium - this is how fast a wave actually gets propagated in the medium in question.
So long as the speed of the wave is faster than than the speed of the source, you're just going to get some distorted version of the original wave...but once the source is as fast or faster than the wave, things gets interesting.