I don't know what the proper name of this nifty doodad is, but I call it the elastic grabber. When you put a piece of elastic between the teeth and then slide the metal ring as far toward the teeth as it will go, it holds the elastic tight so that you can run it through a casing. It's much faster and more secure than using a safety pin, that's for sure. At least for me, that is.
Admittedly, I've lost the end a few times using this tool (mostly because I didn't slide the ring far enough and make the teeth tight enough), but not nearly as often as I've had a safety pin come open and get stuck inside a casing.