Octane rating is the resistance of a fuel to detonate, knock, pinging, or as it's known in the UK and OZ, pinking .
The higher the octane rating, the more the fuel will operate under higher temperatures and combustion pressures, before detonation starts .
To further muddy up the explanation, there are two methods to determine octane rating, one is the RON method, and the other is the MON method .
Here in the US, regular unleaded is 87 octane, mid grade is 89, and premium is 91 .
Octane rating has nothing to do with the fuel burning hotter .
Here in Phoenix, I have to go to 91 octane to prevent detonation due to the high air temperatures here during May-October .
I don't have the link handy, but go to Wikipedia, and put octane rating in the search box, and you will get more info than you know what to do with .