It's a slang term used to describe a player who has lost all of their chips or has been eliminated from a tournament. When a player goes bust, they are out of the game and can no longer participate in the current hand or tournament. Going bust means that a player has no chips or money left to wager, and they are effectively eliminated from the competition.
The term busto is a less common variation of bust. It has the same meaning. Both bust and busto can be used to describe a player's elimination in poker.