Though this phenomenon is probably best described by pages upon pages of differential equations, my best simple explainantion is this: Think of a length of chain hanging and not moving. If you hit it, something like a wave will propagate away from the point at which you struck. Now fix yourself to a point on the chain, start it moving, and hit it again. From your perspective the wave propagates as before, at equal speed in both directions, yet from the perspective of a fixed external observer, the wave's speed and the chain's speed add in one direction along the chain, and subtract in the other. So for chain speeds close to the wave speed, waves will appear to sit at the same relative position or to move slowly along.
This "slowing down" effect is one of the reasons why I am so fascinated. In the moving chain, shapes that would otherwise change too fast to enjoy can be clearly seen.
The Exploratorium has a similar exhibit called the Lariat Chain.