Octane Rating: The octane rating of a fuel determines the propensity to explode rather than simply burn when mixed with air and ignited.
Exploding is bad. Burning is good. The higher the octane, the more resistant to exploding.
If you are running on a fuel with too low an octane rating for your motor, you will get 'pinging'. This, in its extreme form is also known as detonation. The fuel/air mixture is igniting all at once and exploding instead of igniting as a flame wave. The resultant "bang" is very hard on the internals of the engine, including the piston and cylinder heads.
The octane rating is intended to quantify a comparison of the particular gasoline to pure octane - the liquid form of straight chain eight carbon saturated hydrocarbons.
This liquid was given the rating of 100 (100 per cent octane) early on in the research of internal combustion engines and fuels, because of it's excellent ability to resist detonation due to the heat of compression.
A motor fuel is given a rating based on the average of two "measures" of it's ability to resist pre-ignition.
An octane rating is not a measure of quality, only a measure of what compression ratio the fuel can withstand before it will combust without the benefit of fire from a spark plug.