How can a signal travel faster than the phase of a wave, or individual particles?

I remember having a really hard time with the concept of a signal traveling faster than the phase of a wave or than individual particles when I first heard about it during my first year at university. I know my physics professor had an example he thought would help us, and I remember that it was something about being on a playground and stepping on something, but I remember that even then I didn’t get what point he was trying to make.

Anyway. I have blinds in my living room, and whenever I open or close them, I somehow think about this. In the movie below you’ll see me crank the blinds up and down. From the reflection of the lit door in the background you can see that the camera stays in more or less the same position during the movie (yes, dad, next time I’ll use a tripod!), and from the sound you hear that I’m cranking with more or less the same rate throughout the movie. And yet you see the blinds seemingly move with two different velocities: One when all the panels move in parallel, and one when the signal that something started moving (or stopped, as in the second case) propagates through the blinds as the gaps between the panels open or close.

Now tell me: Is this a good example? Or why not? What would be better?