If you use external flashes with your SLR then you'll know that getting them off the camera hotshoe is the best thing you can do - who wants a shot with on-axis light, it's boring!
With a flash bracket you can screw your camera into one of the thumbscrews and mount your flash on the other (connected by an eTTL cord or wireless trigger) to put it off-centre and add some more interesting shadows to your portraits. It's not as good as getting it completely off and onto a lighting stand with a softbox or umbrella but it's a good start and it allows you complete movement.
Where it gets really useful though is for macro photography where your lens is often very close to the subject which limits the light reaching it - if you have a flash mounted on the camera then you're likely to get a shadow cast by the lens itself.
The solution? Use a flash bracket like this, coupled with something like a mini ball-head like
CULLMANN - MAGNESIT MINI KOPF which allows you to angle the flash parallel to the lens and bent inward towards your subect. If you use an eTTL cord such as
TTL Off Camera Shoe Cord for Canon 580EX II 550EX 430EX II 380EX then your camera will automatically calculate the correct flash exposure even though it's now much closer to the subject than usual, or pop it into manual mode to get creative!