The Suck Box is the name given to a repository where cards that are no longer used for playing are placed, as opposed to just throwing cards away (or recycling, if you're eco-minded). These are usually the cards that didn't make the cut during the postgame judging, although cards that involve reviving, condemning, and otherwise manipulating cards to and from the Suck Box during gameplay are certainly possible.
So why not just throw old cards away? The suck box serves as a powerful resource for teaching new players how to create cards, as it may serve as a list of "what never to do, ever again." It may also serve as a visual reminder to avoid creating suck-worthy cards.