The purpose of the Lumiquest Big Bounce is to move the light source from an accessory Flash (such as the Canon Speedlite 580EX Flash, Canon Speedlite 420EX Flash or the Canon Speedlite 550EX Flash) farther from the camera and to soften the light. Lighting coming directly from a small flash head is typically harsh looking on your subject - there will be very sharp, strong shadows.
Using your flash's bounce capability is a good way to give yourself a larger light source. However, there is not always a white wall or ceiling available for bounce flash. This is where the Lumiquest Big Bounce comes in. The Big Bounce is attached to the flash using Velcro (get the Lumiquest Cinch Strap). The flash is fired into the Big Bounce, which in turn reflects the light toward your subject. Since the surface area reflecting the light is larger than your flash head, you get a larger effective light source. The result of using a Big Bounce is a softer, more pleasing light on your subject.
Unlike some flash accessories, the Big Bounce maintains the infra-red focus assist functionality of the flash. Keep in mind that you will loose some power from your flash while using the Big Bounce.
I found the Big Bounce to be the most effective hot-shoe-mounted flash diffuser I have tried for use in a high ceiling (or no ceiling) area. I could see a modest softening of the shadows in typical people pictures.
Unfortunately, the Lumiquest Big Bounce is huge and heavy. I could not get the flash head on my Canon 550EX to stay upright. The weight of the Big Bounce kept pulling it back down with the slightest motion. the Big Bounce's appearance is borderline silly. It really is "Big". I decided the Big Bounce was not for me.