Much like MC Escher's picture "Treppauf und treppab" portrays the optical illusion of a never ending staircase, the Shepard effect is an acustical illusion that gives the listener the impression of an endlessly rising melody.
Acustical perception is less then perfect. By abusing certain weaknesses in the way the human brain processes sound, it can be tricked into believing that it hears an ever rising scale or melody.
In reality, of course, an endlessly rising scale is impossible. The illusion is achieved by playing the same note in four octaves at the same time. By cleverly fading the four scales into and out of each other, the listener won't notice that they are actually hearing the same 12 chords again and again.
I wrote this Java applet (4.5 MB) to visualize the Shepard Effect. You might need to download the Java Plug-in in order to view this visualization.