There are lots of examples of these out in craft world, all pretty much with the same premise - you take a placemat, fold it into rough thirds, and attach them down the side by sewing or with glue. Pretty simple but very effective if you can manage to get a really unique placemat! When I saw this post by Litte Miss Mama a year ago I HAD to try and find a laser cut felt one. And this is what I found at Dunelm Mill:
I attached the placemat to a piece of turquoise felt for a nice contrast.
I then trimmed around the outside so that the edges followed the shapes, folded it two-thirds in and hot glued along the sides, and finished off by adding some magnets to act as closures.