The Black Diamond Ice Clipper is their retort to the Petzl Caritool: a nifty little plastic (i.e. non-load-bearing) carabiner that is designed to rack ice screws (about six of ’em) and tools (one).
The big difference between this and the Petzl model is the Petzl has an integrated clip to secure it to a harness or pack strap. The BD either fits into small loops designed to accomodate it on BD harnesses such as the Blizzard, or you can use the included rubber keeper thingy to attach it to a non-Clipper compatible harness (i.e. almost every other one out there).
Another difference is the BD Clipper wiregate is designed to stay open when you move it all the way back. In practice this sometimes works, sometimes doesn’t. Pluses and minuses: when it stays open it’s easier to manage your screws, but don’t forget to close it! If you have a BD harness, get this one. If not, look at the Petzl.