Bust a Player
To bust a player is to win a hand that eliminates them.
The simple explanation
To bust a player is to win a hand that eliminates him from the game. If your hand beats another player's and he has no chips left afterward, you have busted him. Players may say 'I busted him' or 'he busted me'.
A closer look
In tournaments, busting players is the way to move up the standings and sometimes to win a bounty. A player who busts another is said to have knocked him out. Getting a hand through to showdown against a player who is all in is the usual way. The player who is busted is eliminated; the player who wins keeps the chips.
A practical example
A player wins an all-in hand and busts the opponent.
Full explanation
To bust a player is to win a hand that eliminates them.
To bust a player means to win a hand against him in such a way that he loses all of his chips and is eliminated from the game.
The term is often used in tournaments, where players are eliminated when they lose all their chips.
In bounty tournaments, busting a player earns a cash prize in addition to the chips.
The same event seen from the other side is to bust out.