Low octane fuel is like pistol powder... fast burning, and touchy when you're pushing the limit. You can get detonation (knocking) more easily. Modern computer controls keep the detonation under control, but your bullets will be slower when it does.
High octane fuel is like slower burning rifle powders... the higher the octane, the slower the powder. Compression in the engine is like barrel length... if you use rifle powders in a short barrel, you don't get more bullet velocity (power).. but with the proper barrel length for the powder, you'll get much better performance.