It would protect the edges from scuffs and scrapes like I just experienced from my recent tumble onto a concrete driveway. Cosmetic damage only; but for some it's a valid concern.
A good bumper can do more than protect against cosmetic scratches. A bumper with impact-absorbing gel - think of the
Tech21 case, but without a back - will absorb shock that could prevent some glass fractures if the phone landed just wrong. Not that I would recommend this, but I have seen people bounce their phones off a table edge (tossing the phone down) with a Tech21 case without an issue. If you struck the right or left edge in the same way unprotected, or even in a thin TPU style case, you may end up with shattered glass. It's not just cosmetic protection.
The Tech21 case is probably the closest to a bumper, and I believe it has a transparent back. Unfortunately, it's not a true bumper - you can't remove the back from the case.