As much as I despise Wikipedia, the article there on Octane is pretty good.
Simply put, higher octane PREVENTS pre-detonation (aka "pinging") whereby during the compression cycle of the motor, the gas & air mixture gets compressed. That compression causes HEAT. The heat can be so great that it will ignite the fuel/air mixture before the piston reaches TDC and the plug fires a spark. When that happens, the motor "knocks" or "pings" and it loses power & is pretty hard on the motor.
Conversely, an octane TOO HIGH, will not burn completely and will burn much slower/cooler than a "correct" octane. When this happens, it leaves deposits and robs the engine of power & economy. So those people who feel they need to run 110 octane fuel in their stock motors are not only wasting money, they're killing mileage, losing power and damaging their motors.
The consumer though is basically an idiot and will buy what they "think" will "clean out the motor", "give more power", etc. A few years back I think it was exxon that was sued to have the phrase "Put a tiger in your tank" removed from their premium fuel advertising because it was misleading customers into buying higher grade fuel than necessary.
High octane doesn't clean shit, it doesn't give more power. UNLESS, the motor is designed for it. Then, of course, it wouldn't necessarily be "high octane", it would be "CORRECT octane"...
The correct octane is the lowest level you can use without predetonation.