Using nonscientific terms, the octane rating describes how quickly or "explosively" the fuel will burn. Lower octane is "more explosive," or "less controlled," while higher octane fuel burns in a little more of a controlled and slower fashion.
For higher compression motors or motors with turbos, the controlled burn is important. It allows for advancing the ignition timing and optimizing the spark relative to piston position. If you have high compression and a relatively advanced spark, the less controlled burn of a lower octane fuel can lead to engine knock/ping. This is most apparent when under high loads and temperatures. For a turbo engine, you may have fairly low compression at atmospheric pressure, but spin up the turbo and it's like increasing your compression ratio. For cars with knock sensors, these detect the pre-detonation of fuel (ping/knock) and allow the ECU to retard ignition timing. That's why you often get worse performance with lower octane fuel in a higher compression or turbo engine - the ECU is protecting the engine by retarding the ignition timing.
I typically run 91 octane from my local gas station - no issues at all, but I'm also not in the extreme heat of the desert SW or climbing mountains. 93 octane doesn't seem to make much difference when I do get it. I have a local gas station with 110 octane racing fuel. I haven't tried that yet ($6/gallon) but I suspect nothing bad would happen, other than potentially getting some combustion by-products that would otherwise get burned up with proper combustion (e.g. more CO rather than CO2). Might mess up a catalytic converter a bit. But there would be no benefit to the higher octane unless I could advance the ignition timing, which also relates to the underlying fueling and ignition system being designed to take advantage of it. For a race engine, those are run at the ragged edge, so they can be designed for higher octane - higher compression or boost and tightly controlled ignition advance.
Eville Rich
2016 S10
2015 WR250R