The triple option is easier to understand out of the I.
A basic triple option play works like this:
QB looks at the defensive alignment, and decides whether it's smarter to give the ball to the FB up the middle or keep it himself.
QB takes the snap from under center.
QB either hands off to the FB, or keeps the ball himself, and runs towards the strong side of the field. (towards the TE in the I formation diagram above) The HB runs along behind / outside of the QB while he's running. Do note that because of the fake, one of the LBs is stuck defending the FB.
The TE lays a lead block on one of the linebackers, but either another LB or a safety will come up and challenge the QB. If the QB isn't challenged, he runs forward for 5 to 8 yards. If he is challenged, then he waits until the last second and pitches the ball to the HB.
At the moment of the pitch, one LB is stuck on the FB, one LB is stuck on the TE, one LB (or SS) is stuck on the QB, the CB on that side of the field is being blocked by the WR, so the half back is one on one with whoever's left. Either they tackle him for a short to medium gain, or he breaks it and goes to the house.
That's the basics of triple option football, as it was played by numerous teams for many many years. The thing about it is that you only have numbers running towards the Tight End, so the defense is able to adjust to it.
Paul Johnsons Flexbone trick is really pretty simple. He lines up in that "Double Slot" formation BOR posted above, which is balanced towards both sides of the field, and has 4 guys near the line instead of 3, who could all be receivers if we wanted them to be. (it's supposed to essentially be a 4 WR set, which it is if you have the right personnel). Then he rolls one of the Slot Backs (SBs) around behind the FB during pre-snap motion, and runs the same old I form triple option, since he's now lined up properly for it. The defense never knows who's going to rotate back during the motion, though, so they can't line up to one side, and they also don't know if you're going to put 4 guys out in the pattern, so they have to stay home to worry about the pass. The formation freezes them, which simplifies your reads, prevents them from stacking the point of attack, and overall allows the option to work better.
So it's power football from a spread formation.
To drive the point home, think about it from the point of view of the defense. Usually for triple option, everybody gets a guy. The weakside linebacker takes the fullback, the middle linebacker covers the QB, and the strongside linebacker takes the pitch guy. That way you rotate your assignments so you can stop the run with your linebackers, which is the goal. In the flexbone, nobody knows whether the pitch guy is going left or right presnap, so the middle linebacker's gotta take the fullback, leaving one outside linebacker to deal with both the QB and the pitch guy, and the other linebacker is whistling dixie. You need 4 LBs, or 3 and saftey support, for every running play. That leaves only 3 guys in pass coverage, and your formation has four potential receivers right at the line of scrimmage.
