The video below shows how multiplexing works by slowing it right down.
The display shown is a "scrolling LED" display I bought at (I think) Jaycar a while ago.
I opened it up, and disconnected its internal processor and connected up a Uno (Ruggeduino actually).
Controlled by a potentiometer off camera, I slowly increase the multiplexing speed.
The display has 72 columns of LEDs and 7 rows.
Internally it has 10 x 74HC595 shift registers. Nine of them are used for the columns (9 x 8 = 72) and the last one selects which row is displayed.
As you can see initially, you see one row at a time, as each row is selected. However once running at full speed the persistence of vision effect makes it look like all LEDs are active at once.
http://vimeo.com/80312101Some photos of the internals:


