The term live cards in games like Hold’em and Omaha refers to a hand that’s a significant underdog and likely to lose but could still improve to a winner. So, although behind, the hand is still not dead.
For example, you get it all in with KK on a board reading 7 5 2, and your opponent turns over 7-8. You’re a big favorite to win the hand, but the other player has live cards, as any 7 or 8 would give them a significant advantage.
If they turn an 8, they’re now in the lead, and you’re one with the live cards, as any K, 5, or 2 would give you the winner.
In most cases, if you get your chips all in on the flop or the turn, you’ll have live cards, but sometimes, you could be drawing dead, i.e., have absolutely no outs. For example, you have 5-6 on the board reading 5 6 2 Q, and your opponent turns over QQ. There is no card in the deck that can give you the winner since even if you hit a 5 or 6 for a full house, your opponent will have a higher full house at that point.