The term “live cards” in poker refers to an inferior hand that still has a chance of winning. As long as the opponent has any outs, they have live cards, as they can still win a hand, regardless of how far behind they are.
For example, you are all in with pocket kings against pocket queens, and the board runs clean on the flop and the turn. Going to the river, your opponent still has live cards as they still have two outs they can catch to win.
Holding live cards in an all-in situation is important, as there is hardly a worse feeling in poker than drawing dead, which means that your cards are no longer live as there are no outs you can catch to improve your hand.