What is the difference between high octane and low octane fuel? I'm not asking if one is better than the other for my vehicle, specifically, but rather what occurs differently both scientifically and mechanically when either is used?
So-called "octane number" is a measure of how much the air-fuel mix is resistant to detonation.
The higher the "octane number" is the more resistant it is and the more is can be compressed without exploding. The higher the pressure is at the point the air-fuel mix ignites the more efficient the engine works.
Modern engines are designed for some rather high air-fuel mix pressure, if the mix ignites before that pressure is reached the engine just won't work right, because ignition will happen at the wrong moment of the engine cycle. That's why only fuel with right "octane number" should be used for any engine - depending on how that engine is designed, otherwise it just won't work right. The vehicle manual usually specifies which "octane number" is right for that vehicle engine.