I think it's a duster for powdered sugar, cocoa powder or other light-weight decorative dustings. The light-weight powder is kept under control by the lid, thus no cloud of yuck all over your counter. It's held over the object and tapped on the lid to give an even distribution. You've seen the fancy brownies with the nice, even dusting of white powdered sugar, right?

When you're between dustings, put the lid, clean side down, on the counter and place the sifter on top of it to keep your counter clean.

Do I win? Is there a prize????

ETA: Hey, it just occurred to me that if the lid actually fits securely, you can just leave it on and set the whole thing down on the lid side. Maybe that's the "special" aspect of this very unique item. Myself, I use a regular old stainless strainer and a measuring cup to hold it while I don't need it. I'm not a fan of dedicated tools, they're a wast of my precious space!