When should you use the Multi/Stroboscopic flash mode on a Canon 580EX II?

Stroboscopic flash (Multi mode on Canon, Repeating Flash on Nikon) fires several flashes within short time, by using shutter time long enough you can capture them all. You can calculate needed shutter time (in seconds) by dividing number of flashes by frequency in Herz. For example, 10 flashes at 5 Hz takes 2 seconds to fire.

Typical application is single-frame chronophotography - capturing several phases of movement on same photo. So a suitable situation is where some interesting movement occurs. If the subject stays in one place during its movement (e.g. a dancer spinning), you can slowly pan your camera instead to have different phases recorded on different locations in your frame.

A variation of this is capturing the same subject from several angles on single frame by moving your camera around it while the flash is strobing. The subject is still, but the camera is moving. So a suitable situation is when there are several views of the same subject you want to show simultaneously.

For these techniques, dark background and light-colored subject tend to give better results.

Another case would be when you want to imitate multiple flashes with one flash and you need constant frequency to form a pattern - when your flash is moving at constant speed this will give you flashes at equal distances:

If you don't need constant frequency, manually triggering the flash (e.g. with "Test" button) will give you more control over the outcome.