Ok, I'll bite. It looks like a chuck, but the jaws are threaded, so it must be an adjustable die of some sort.
What's it commonly used for, and what's its proper name? )
M
It is a Geometric threader, there is also a rubometric in the box.
http://www.youtube.com/watch?v=JSMWLpx4rS4 is a pretty good example.
Steve