In the magazine business, bind-in cards are the thin cardboard subscription cards or other advertisements that are bound in with the rest of the magazine, and usually perforated for easy removal.
The physics of bind-ins is rather interesting: if the ratio of the thickness of the bind-in to the thickness of the magazine page is sufficiently large, and especially if the magazine is bound with staples (e.g. Business Week or The Economist as opposed to Wired) they have the they have the rather annoying property that they prevent the reader from quickly flipping through the magazine to a specific page; the extra weight causes you to "snap" to the pages next to the card. Curiously, most magazines use bind-ins to provide subscription cards to a magazine you're already getting.
Compare blow-in card.