Like Kenny said above, the higher the octane rating the more stable the burn. That's why high compression or high boost engines will use race gas to lower the chances of preignition and detonation.

If you want to see the affects of the octane rating and the different ways they burn you can try this. Two test tubes, one with 87 octane and one with 93. Light them both and watch the results. When done right you will be able to watch a nice steady, controlled burn from the 93. The 87 will be violent and usually blow up the test tube. That will also help explain what Ryde or Die said about the possibility of making less power from race gas if you don't need it.