On a conceptual level, maybe here’s the thing to understand, and the Grantland article illustrates: Kelly (and others like him, he’s just example 1a of a trend) takes what traditional offenses do in 3-4 plays, and do it in one.
A traditional offense has core plays it wants to run, and then other plays that are based off that. So maybe your core play is an off-tackle run from an I formation. One complement of that is a counter play, where the RB takes his first step like it is an off-tackle run, then breaks the other way. Another complement would be a play-action pass, where they fake that off-tackle run, but then throw the ball. The idea is to get the defense trying to stop play A, and then run play B or C (or D or E). The offense and defense are constantly trying to outguess each other as to which one is coming. That’s what QBs are doing at the line when they’re pointing and changing the play … they started with A, but after seeing the defense lined up, they switch to B or C or D.
In Kelly’s offense, A and B and C are all being run at the same time. Again, read the Grantland article to see this explained specifically. On the one play, they may have an off-tackle run by the halfback, a counter play (in the form of the QB keeping it himself), and a play-action pass (or two) all already built in. Thus there is seldom a need for the QB to change the play at the line – whatever the defense is doing, the proper response is usually already built into the play, the QB just needs to be able to make the right decision.
The irony of everyone talking about how many snaps the Eagles take, is that they will probably run the fewest number of plays of anyone in the league – Kelly has a short playbook, and often runs the same play again and again. It doesn’t *look *like the same play on TV, because one time the back gets it, another time the QB keeps, and another time he throws it … but the call from the sideline was the exact same.
Kelly has said the ideal QB for his offense would be Rajon Rondo. His plays look like basketball plays, with a sequence of if/then commands, rather than a single, definite course of action.