Trading cards are cards with pictures and information which are intended to be collected and traded. They originated as tobacco premiums in the 1800s, but later got packaged with bubble gum for a more youthful audience. (A leading manufacturer, Topps, continued to include a rather awful stick of bubble gum in their card packs as late as the 1990s to continue that tradition.)
Some cards have become highly valuable to collectors, such as the Honus Wagner card pictured, which sold for millions of dollars. In the 1980s and 1990s, there was an explosion of card series catering to the collector market with all sorts of gimmicks (such as hologram cards), leading to the usual boom-and-bust cycles of any manipulated market.
Baseball cards (featuring a picture of a player on one side and various statistics, biographical info, etc., on the other) are the longest-lasting and best-known form, but card series have been issued on every conceivable topic.
One innovation of the late 20th century is "collectible card games", which combine the concepts of trading cards and playing cards to produce cards that are used in a game, such as Magic: The Gathering and Pokémon. (However, kids have long had various "flipping" games to play using baseball cards and other trading cards.)
And, to finally make the whole thing vaguely relevant to a site about file formats, somebody has figured out how to create a Turing-complete computing device out of Magic cards being played in accordance with that game's rules. So you can in fact store and manipulate files this way, even if that would be a really nutty way to do it.