buttons are 88x31 gifs that are and were used to link to another site or another page on your site. this is essentially your "stamp" if you will. some of these buttons are just for fun, some of them are online buttons, some of them are site buttons. these buttons are from past and abandoned websites.
back in the day, there were such things as "districts" on geocities. these were separated in blocks, where webpages were designated by numbers in a specific district and/or block. there were also buttons for your site to indicate which district you were in! you can read more about geocities districts here, which is also where i retrieved them.
stamps essentially serve the same purpose as blinkies, yet they have different dimensions and aren't always gifs. they were popularized by deviantart, but appear on other sites as well.