An external flash has a multitude of uses. You can use it indoors to take photos and bounce the flash from the ceiling, wall, floor, window, whatever to give interesting lighting to the image. It also, when bounced, gives a more even light than using the on camera flash and is less direct.
An external is also further away from the lens so if fired directly toward the subject, the chance for red eye is dramatically reduced. It's a more powerful flash so if you want to take a picture in the harsh sun, it can act as a fill flash to reduce the shadows. Also, when shooting a mixed subject, like people and a sunset background, it will allow for you to meter off of the sun and still brighten up the foreground as well.
I've never personally used the Canon ring flash but know people that do and it is great for taking macro images. It acts sort of like a round florescent (sp) bulb that lights up a close subject for you to capture detail and have excellent lighting. Otherwise, you either have to use natural light or bounce something and hope the light covers it. The on camera flash will usually be blocked by the lens when wanting to take a macro shot.
Hope all that mumbo jumbo rambling helps.
ETA - sorry for the repeat there. I type a lot slower than JDP
