This is one of those things that I think we all know in theory, but rarely use in practice. So I thought this example might show that feathering is as much a valid light modifier as umbrellas and snoots.

All three people in this photo were lit using one light:

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My first attempt at lighting the photo involved trying to position a light stand to frame right, roughly equidistant to all three men. But that meant standing it in a lake and despite prolonged efforts it just wasn't happening.

The only other place I could sensibly position the light stand was behind me. So that's what I did. But that meant it was a lot closer to the guy in the foreground than it was to the guys in the background, so light fall-off was going to be a problem.

To explain:

Suppose I set the light correctly for the guy in the foreground at f/11. The guys in the background were about three times further away so they'd only be getting enough light for an f/2.8 exposure. Or something like that! My knowledge of the inverse square law is a bit shaky but the bottom line is that they wouldn't be getting enough light. Nowhere near enough.

The way I decided to work around this was to set the flash power for the guys in the background, but then turn the flash away to the right. There was still a good chunk of the beam hitting the guys in the background but the guy in the foreground was only getting a thin sliver from the side of the beam.

End result: Everyone got an equal amount of light.

Here's roughly how the set-up was arranged: 

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Feathering is a technique that you should keep stored away in the back of your mind, like the gadget in your gear bag that you hardly ever use but when you need it, you really need it. As illustrated by this example, feathering can allow you to get a shot that would otherwise be impossible to light.