Definition of bust (out)
The fact of "bust" out is to be eliminated from a tournament. In tournaments, you're alive to the last chip. When you lose a pot in which your last chip was, you'll be called a "bust" out in the tournament. If the player who "bust" out finished in the paid seats, he will be able to say that he has "bust in the money" or "I have bust outs in 5th position". It is also possible to say "bust" out with paid seats or before the final table. We will usually specify at what point in the tournament we have "bust outs".
The psychology of bust out
Getting out of a tournament is always frustrating. Some bust outs are more frustrating than others. If you are playing a tournament with 5000 players in which there are 500 paid seats, you won't be upset to finish 3752nd in the tournament on a standard game. On the other hand, if you are at the World Series of Poker just before the money and you "bust outs" of the tournament in 107th position when there were 100 paid seats, it may affect you more. If you play tournaments regularly, this is something that will happen to you on a regular basis, so you might as well get used to it.