It's not a button. It is a US Army brass collar-insignia disc insignia.
Specifically, it is a US Army Infantry Enlisted-man's collar-insignia disc, type 5. If the flat "board" across your disc's back is made of iron (test it with a magnet), it's from World War Two to 1951. If the "board" is made of brass, it's from 1951 to 1970.