The octane rating is not exactly a measure of how fast the fuel burns, but of how fast it autoignites when a fuel-air mixture is compressed. If it ignites too fast (low octane rating) you will get engine knock (detonation at the wrong time in the engine cycle, which degrades engine performance and can damage your engine).

The reason some high performance engines use high-octane fuel is that you can get more power out of an engine if you compress the fuel and air more. More compression, however, requires a fuel that has less tendency to autoignite. High-octane fuel does nothing for you except keep your engine from knocking. It does not contain more energy or burn cleaner.