If this is too long, I apologize but there's three key concepts or ideas for why Josh Heupel has such an elite offense. It's called the "Veer and Shoot" offense. Art Briles made it famous at Baylor with the lack of talent at Baylor. It's a mix of the Run & Shoot offense, the Air Raid offense, and the RPO game. Add in some Rich Rodriguez "spread run" elements and finish it off with Chip Kelly hyper-speed concepts, you got Heupel's version of the "Veer and Shoot" offense.
1) Tempo- This is the most obvious. When you run tempo, it makes it harder to line up, get the right defensive calls, etc. This gives Tennessee a lot of options. They run one play words and use quick signals to get in the call ASAP, then the defense cannot adjust and you can't get set (Tillman's long TD vs. Alabama being the obvious example). Not only that, you lead to tired players which also slows the pass rush specifically. Tennessee practices tempo as much as anyone in the country and simplify their playbook because they believe that quantity is just as important as quality.
2) Choices- RPO's and choice routes specifically. When you don't have completely set routes or play calls it puts your players in position to read the defense and react accordingly. Tillman is phenomenal at this (it's why he seems to be always open. Also explains why sometimes our QB's miss the deep ball. It's harder to throw 50 yard bombs when you aren't sure that's what you're going to do on that play). Heupel and his staff focus more on reading the defense than offensive concepts. If a player does "X", then you do "Y". Heupel doesn't run as many RPO's as you think. A lot of it is designed play action (Kiffin runs a ton more RPO's for example). Either way, WR's aren't held to concepts and this helps the offense. If the defense calls the right defense, you can still make plays because the WR isn't tied to one route ("hey this guy is playing bump-n-run, so I can run a fly instead of a curl).
3) Extension- This means two things: wide splits and using WR screens as run plays. It's my favorite thing about the veer and shoot offense. The wide splits makes the DB show his coverage or declare his coverage. This gives the offense an easy read especially with the quick no huddle. You also spread the field and makes the defense cover everything. You make the safeties have to either guard closer to the hash marks (hence the wide open fly routes) or make them guard the sidelines (hence the quick TE pop plays and why Hooker has so much room to run). Heupel usually goes "11" formation (one back/one TE...a lot of veer and shoot coaches like 4 WR looks, but Heupel knows he can't get away with that in the SEC). Sometimes Tennessee doesn't run the ball well (see the Pitt game). So what does Heupel do? Use quick WR screens for easy runs (Hyatt's 11 catches for 78 yards against Pitt). Those stack formations are dangerous because you can't put two CB's close to the LOS or else you get picked and rubbed to death. So one CB has to play back, you get the ball out quick and your WR blocks the CB for 5-8 yard gains (and sometimes more). With the safeties playing deep, the LB's playing closer to the box because of the run game and those stack formations stretched out so wide, you get quick, yard churning plays to stay on schedule.
This is a very simplified version but it basically is the core tenets of Heupel's offense.