Definition of bust (out)
To "bust" out is to be eliminated from a tournament. In tournaments, you are alive until your last chip. When you lose a pot that your last chip was in, you are said to have "busted" out of the tournament. If the player who "busted" out finished in the paid seats, he or she can say that he or she "busted in the money" or "I busted out in 5th place". You can also "bust" out with the paid seats or before the final table. We will usually specify at what point in the tournament we have "busted out".
The psychology of the bust out
Getting busted out of a tournament is always frustrating. Some busts are more frustrating than others. If you're playing in a 5,000-player tournament with 500 paid spots, you won't mind finishing 3752nd in the tournament on a standard play. However, if you are at the World Series of Poker just before the money and you bust out of the tournament in 107th place when there were 100 paid spots, it may affect you more. If you play tournaments regularly, this is something that will happen to you regularly, so you might as well get used to it.