This is a *really* nice, simple app. All it does is present (or should I say: simulate) a nice, clear uncluttered background. In reality, of course my desktop is a mess, and there are usually more windows open than I can count.
Backdrop simply puts an image (be it a white pane, or the original desktop background, heck even a simulated background with documents, drive and dock) above everything, so your frontmost running application *looks* as if was the only app running on your Mac. The image extends to all connected screens, effectively covering your entire desktop.
To me this is important for two tasks - when I create imagery for documentation that some poor sod has to write, and when we create videos that show how to use an application (hey, there is a market for it - don't knock it).
Instead of having to to create a separate user or clean up my desktop (that will *never* happen), all I need to do is put up a nice empty image, and begin rolling the video (or in the case of stills, take screenshots).
But there's another, unexpected use I got out of this app: when designing or color grading images, I keep the theme color as a reference above everything else (some kind of 'full screen mode except it's not fullscreen) that blocks everything but the color grading app and constantly shows the reference color (easy to compare, easy to pick up with the dropper tool). Sure, only saves a couple of clicks, but they do add up...
I've been using Background for a couple of years now (from when its Icon still was a theater), and am aware that there may be newer, competing software available. I'm simply happy with this, and will stick to it until it breaks compatibility (I'm currently running on 10.6.8).
Definitely give this one a try.