Man defense means that each defensive player is responsible for covering one offensive player or “man”. Man defense helps to better ensure that no offensive player is left wide open (which can happen in zone defense). Football is a chess match and calling a man defense is part of a strategy. The defensive coordinator knows that no offensive player should be wide open and that the opposing quarterback will have throw an extremely accurate pass to get a completion.
Now all of the pieces of the puzzle have to fit together in order for man defense to be effective. First, the defensive players covering the offensive players running routes must stay close enough to their man for a long enough time to allow the defensive players rushing the quarterback to get to the quarterback. Second, the defensive players that are rushing the quarterback must get to the quarterback before one of the offensive players running routes gets free from the defensive player covering them (“gets open”).