It comes from huygens principle. Each point of a wavefront can be treated as a point source for a wavefront. They seems to form a common wavefront because they interact with each other through a phenomenon called interference.

This leads to a wave entering into a lower impedence media to be refracted away from the normal of the surface, you can view it as a car which comes from driving in mud into driving on good ground with one wheel first, that wheel will get better traction and the car will turn as it is now moving faster than the other wheel. At a certain angle the car will turns so much that the other wheel never passes the boundary, the car is deflected.

You could see it as the first wheel being a part of the wavefront which passes the boundary then starts interfering with the wave point sources still inside the media causing the aggregate wave front to not pass the boundary. Maye one could say that they interfere with their own potential to travel faster beyond the boundary.

Sound is not my speciality though I'm more used to thinking probablity waves so someone else may have a better explanation. But it should work the same, all waves act in the same way.

Edit: Also something about the energy being indestuctible and dependent on the frequency (which means the frequency cannot change) and the sound moving quicker and/or slower which means that the wavelength change in diffrent media. It's been almost ten years since I worked with waves.