Myth: Higher Octane gas burns better, hotter and provides more power.

The basic need for understanding octane ratings comes down to
one statement for firefighting....
"Class B rated foams work equally on
all three common gasoline Octane ratings".

Octane rating - Measure of a fuel's resistance to detonation (Knocking), or the premature ignition of the fuel/air mixture during the engine's compression cycle.
Octane rating does not relate to the energy content of the fuel.  
It does tell how much the fuel can be compressed before it spontaneously ignites. This is why higher performance race engines require a higher octane rating fuel.
Carbon deposits and pits in pistons leave small amounts of fuel which pre-ignite (Through heat of compression) causing "pinging". Pinging is also caused by using a lower octane fuel than recommended by the manufacturer. Anti-Knock or other additives increase the octane rating of fuel to help reducing pinging.

Ever notice the (R+M)/2 label on a gas pump?
This is an average octane between a European standard of pre-ignition/octane rating (vehicle not under load) and an American standard which rates pre-ignition with vehicles pulling something or under a higher load.

Internal combustion engines are designed to burn gasoline in a controlled process called deflagration. But in some cases, gasoline can also combust abnormally by detonation, which wastes energy and can damage the engine. One way to reduce detonation is to increase the octane content of the gasoline, which is expressed by its octane rating.

Normally a spark plug fires, providing the "HEAT" side of the tetrahedron. Heat from compression may be enough to "fire" the fuel vapor which will not be properly timed with the complete engine cycle.

A higher octane fuel is needed with a higher compression such as in a performance car. If you have to run a higher octane fuel than your owner's manual calls for to reduce knocking and pinging, it could be a sign of several other engine problems.