The boxed card term refers to a card that’s turned the wrong way in a poker deck. It’s a card showing its face-up value during the deal. Most poker rooms treat boxed cards as dead, and they remove them from the game.
If this happens, the dealer will give the player who would receive this card the next card from the top of the deck. The boxed card is put in the muck.
For example, you might encounter this while the dealer is shuffling the deck, and they accidentally shuffle one or more cards in the wrong direction.
This can even happen when using shuffle machines. It’s simply an honest mistake that can happen from time to time.