The different roles and responsibilities of the players are explained here:
Defensive Responsibility:
The primary defensive responsibility as with all formations employing 4 defenders lies with the two centre backs. The 2 full backs are also required for defensive responsibility against the wide attacking players of the opposite team. Similar to the 4-2-3-1 formation, amongst the midfielders, the central midfielder plays a role of covering the defence by breaking down play and tackling. The other two mid-fielders are also required to contribute to defending.
Midfield Play:
The midfield play involves the two wide midfielders to play box-to-box football. The full backs are also required to play higher up in the field during attacking plays. However, as opposed to the 4-2-3-1 formation, the full backs play a more supporting role in midfield than attacking and centering the ball. The three midfielders usually move as a lateral unit when the ball possession is with the opposition. This creates a wall in the midfield and the holes in this formation are required to be anticipated and covered by the defenders. When ball possession is achieved, the two wide midfielders move up higher in the field to run into the box to receive the centered balls.
Attacking Roles:
The central striker is the pivot of the attack. He should have the ability to run into the box and head in centered balls while also being able to hold the ball to bring the other attacking players into the game. The main responsibility of the wide players is to stretch out the opposition defensive. The wide attackers should have the ability to dribble the opposition full backs and cut in or centre the ball. The likes of Messi for Barcelona or Arshavin for Arsenal were good examples. The wide midfielders are expected to make runs into the box to support the striker when the wide attacking players make their wide runs.
When playing the 4-3-3 formation defensively, often teams are seen breaking into the 4-1-4-1 formation. This is done so that the wide attacking players can drop deep to cover defense. All in all though, the formation is effective for playing quick and attacking football. Counter attacking is easier due to the presence of 3 attacking players. However, as of late, this formation is rarely employed. Real Madrid has been using this formation successfully for a few seasons now and off late, Brendan Rodgers has successfully used the formation for Liverpool as well. However, this still remains as the 2nd most popular formation to the 4-2-3-1 currently.