They are button badges that you can put a custom image inside of. Some folks use it for a favorite anime character, tv show, etc. Lots of people make and sell custom badges on Etsy but if you have a craft store or a Daiso store nearby, you can also make them yourself.

I bought a badge kit yesterday along with some other materials.

Or if you plan on making a lot of them to sell at a con, you can get machine like this one.