That, sir, is a Millers Falls corner brace, and a very useful tool they are too!
It allows you to drill a hole right into a corner! Although largely superseded by power tools, especially the right angle drill, nothing can get closer to a corner than these!
Many serious craftsman prefer a brace to a power tool as it gives them more control, and of course these tools will still be giving good service long after most power tools have died!
Millers Falls were a U.S. manufacturer of top quality woodworking tools. Their heyday was in the 20's and 30's and their tools were top end! I have a few still in use today and wish they were still available! if you think of Millers Falls as the woodworking equivalent of Blackhawk you won't be far wrong!
In the U.K. people are starting to buy up tools by these older makers for restoration. Their biggest customers seem to be users who can't find anything as good new!