This item is called a fore-edge clamp, and it's designed to display the secret fore-edge paintings on your books. Needless to say, it's incredibly expensive, but if you can afford a collection of books with secret fore-edge paintings, you can spring for this.
A secret fore-edge painting is one that is revealed only when the pages are pulled back as shown. When the book is fully closed, only the gilt edges appear. Here is a magnificent 1898 fore-edge painting of a whaling scene from the Colorado State University Libraries Rare Book collection.
Some books have double fore-edge paintings, so that one picture is displayed when the pages are spanned in one direction and another when they are spanned the other way. There are also triple fore-edge paintings. In this case, the edges seen when the book is closed are not gilt, but have a painting on them as well.