There are two types of full court trap: man and zone.
In a man trap, the goal is to check up on someone and force them to the sideline. By forcing them to the sideline, you are allowing yourself to set up a 2-man trap. Once you force the trap, you can force turnovers.
In a zone trap, the goal is to force the ball handler to make certain passes or dribbles. Once they put the ball in a trigger spot (past half-court, wing, corner, etc.), then the double-team comes and you can force a turnover.