You may have noticed, if you've watched any game of the Les Miles era that LSU has a way of running the football that is unlike any other team. LSU pitches the ball on all of their normal run plays. In terms of the actual blocking scheme, there is nothing inherently different that LSU does when running these pitch plays than anyone else does when handing the ball off. The offensive line, tight ends and running backs are working the same tried and true zone and gap scheme that most every team runs. The difference is that when the LSU quarterback lines up under center, he often will turn and pitch the ball to the back instead of handing it to him. I've written about how LSU does this (here) and Ian Boyd has two great articles on blocking schemes (zone and gap) so I don't know want to bore you by repeating the details. Instead, we'll take a look at why LSU does it.
In most sports, playing defense is simply about restricting the time and space of your opponent. You want to constrict your opponents to a certain area on the field by having more of your guys in that area than they do. This is true in football as well. The more people you put at or near the line of scrimmage (the box) the more chance you have of stopping the run. It's a numbers game. Put more people in the box then they can block and you'll have a chance to shut down any run game.
The benefit that defenses in the days of your grand pappy had was that because when the quarterback turned his back to hand the ball off, the defense could actually do out number the offense. They could add one more player than the offense could block because the quarterback didn't need to be accounted for. For example, when LSU goes under center to run their pitch plays, the personnel they use is often 2 running backs and 1 tight end. This gives the offense 7 potential blockers and 1 potential ball carrier. The defense can now put 8 defenders in the box and still feel comfortable with 3 pass defenders against 2 split out wide receivers. 7 defenders to take on blocks and 1 extra guy, presumably, to tackle the ball carrier. Against an attack like LSU's you'd want to take your chances and bring that extra player into the box because throughout most of the Les Miles' tenure (and definitely the recent past) LSU's passing attack hasn't been able to consistently win using the numbers advantage they now gain in the defensive secondary.
When you add the quarterback to the running game, the numbers even out. All of a sudden you have a man for a man even if the defense decides to bring an extra player into the box. So then how do you actually add the quarterback to the run game from under center? You run the veer (read: option). Wishbone, I-form, Flexbone, whatever formation you want. Whether the quarterback gives, keeps or pitches the defense has to account for everyone in the box. The problem with these classic option offenses is that it puts the quarterback in a lot of danger. The quarterback is taking a licking every play. He's running dangerously close to a lot of bigger men than him. While theoretically, running under center option play is the answer to the question of how to defeat a loaded box, practically, it is not. From a personnel standpoint (that standpoint being that the QB is the most important player on the field) it's not going to be most teams preferred way to do this.
A lot of teams who go under center just feel like they have to live with being outnumbered in the box if defenses choose to. Of course, if you can throw the ball from under center, you'll have an advantage in the passing game. If a defense loads the box, it is forcing itself to play a 1-high safety defense. This limits what it can do in coverage and most offenses should feel comfortable throwing against that. In the running game, you live with a rolled down weak safety tackling your running back after 4 yards rather than him getting 6. Make them pay in the passing game. LSU, however, has decided that they still want to find a way to use their quarterback in the running game without running under center option. To do this, they use their quarterback as an extra blocker after he releases the ball. If he were to turn to the running back, stride over to him and hand the ball off, it would be too late be too far from the line of scrimmage to effectively block anyone. To counter this, LSU QB's pivot from the center, pitch the ball to the running back and then pivot to the backside of the play where their blocking scheme has left them to pick up any backside pursuit. It's that simple. LSU just "blocks" the backside player.
Honestly, I don't think it adds a lot of value. Last year, Brandon Harris blocked no one on that play. He didn't even force the backside defender wide and over the top of him most times. Why would you want your quarterback blocking anyone anyways? Furthermore, you can't play action out of this look so there goes your bootlegs, waggles and keepers. The play works because it ends up just being a regular zone or power/counter scheme. Nothing more, nothing less. A team like LSU can deal with an extra defender in the box because they have elite players at running back and offensive line. At least, it looks cool.
The main aspect of the pitch is that the ball gets to the running back faster. Although it could be argued that what you make up in time, you lose in vision. With the ball being thrown at the ball carrier, he must visually locate it and corral it. When he is being handed the ball, he can keep his eyes up on the blocks. The difference is probably negligible but this might be another reason why LSU decides to pitch it -- they clearly practice it quite a bit.
The play isn't some secret behind LSU's success. LSU manballs people to death through power and force not fancy scheme. When you see the power pitch or zone pitch don't focus on the pitch, focus on the actual blocking scheme to gain a better understanding into how LSU runs the ball.