Octane is, among other things, a rating of how resistant to combustion fuel is. Higher octane fuel is more resistant to combustion, and is thus suited for use in high compression engines.

Think about it this way: a naturally aspirated Honda Accord only requires 87 octane fuel. If you put a turbocharger on that same engine, it will require higher octane fuel because you are increasing compression.

Generally speaking, an engine designed for high octane fuel is also designed to function with lower octane fuel, but it will produce less horsepower. An engine designed for lower octane fuel does not produce more horsepower with higher octane fuel.