THE SETUP
Shortly after the snap, a yellow flag goes flying and the stadium sighs as it realizes this is probably a lost play. Inevitably, your running back will hit a crease and go for 17 yards or the quarterback will hit a wide open guy 25 yards up field. You shake your head as the team ends up walking five yards backwards from the previous spot, pondering whether lining up correctly is a problem in practice too.
WHAT IS THIS CRAP?
This rule is on the books to help provide structure for the game. I wouldn't be surprised if it was there for safety as well, to help keep the number of high speed collisions down.
When lining up in a formation, the offense must have at least seven guys on the line of scrimmage. You can have more than that, as you often see in goal line situations. However, you can't have fewer than seven. Since receivers are usually the ones who mess this one up, power rushing teams don't see this one as often.
This is a legal formation:
The five offensive linemen are on the line of scrimmage. So are the X receiver and the Y receiver, who happens to be a tight end. The Z receiver, quarterback, fullback, and halfback are all off of the line. Seven on; four off. Nothing is wrong with this formation.
This, however, is an illegal formation:
Here, the tight end moved off the line and back into the slot. This leaves only six men on the line: the X receiver and the five offensive linemen. One of two things was supposed to happen: either the Y or the Z was supposed to be on the line but had a brain fart and didn't.
There really isn't much excuse for one of these penalties. It's always a player's fault too because offensive coordinators don't draw up plays with illegal formations (or if yours does, he's even more incompetent than you thought). Maybe he's a noob who doesn't know his playbook yet, or maybe he just flaked out. Either way, he's up for a good chewing out session when he returns to the sideline.
One last bit of red tape: on a regular play, you have to have at least five guys on the line of scrimmage wearing a number between 50 and 79, inclusive. You can have more if you like, but never fewer than five. If you have less than five, that's also an illegal formation.