Busted is a term referred to when a player is arrested in a GTA game.

Many things can contribute to this:

Getting pulled out of a car/ bike/ helicopter/plane/boat
On the ground as a cop is standing over you (mainly in hand-to-hand combat)
Getting knocked over while trying to steal a cop car (while a cop is inside)

Note: The only way to get busted is by attaining a wanted level.

Effect

As a result of getting busted you'll lose all your weapons (except in GTA San Andreas when you have Barbara Schternvart as a girlfriend) and fail any mission you were on causing you to start over again.

Extra

In Grand Theft Auto: San Andreas, when Carl Johnson gets busted, he will respond either positively or negatively depending on the wanted star levels at the cop.