First off, you've done a great job cleaning this clamp. It looks really pretty.
C-clamps with the wings are sometimes called carriage maker's clamps, which will tell you something about the use of this design. As for the rest of it's uses, some wood worker told me years ago, "You can never have enough clamps." At the time I thought that was kinda silly. But it wasn't long until I found I had nowhere near enough of them. Now I have a milk crate full of C-clamps, and bar clamps and pipe clamps and Jorgenson wood clamps, some tiny brass bar clamps, edge banding clamps.... Sometimes I still run out. They hold things in place while you work, they hold pieces together while glue sets, they crank things together so you can fasten them. A couple of clamps working together can hold a piece so you can work on it at a convenient level or angle. They work so well, I think, that collectors take them for granted. But check the prices on new ones. I'd rather pay even a little more to have one like yours.
That's a right fine C-clamp!