*Warning* Lecture Follows *Warning*:
Advancing the timing actually doesn't get any more air into the combustion chamber, all it does is maximize the efficiency of the combustion when the sparkplug lights off. Since the flame front/pressure wave of the ignited mixture takes a little bit of time to travel downwards from the cylinder head towards the approaching piston, if the plug fired exactly when the piston was at Top Dead Center then some power would be lost since the pressure wave wouldn't reach the piston until it was already withdrawing down into the cylinder.
Soooooo, Firing the plug a certain amount of time before the piston reaches TDC results in the combustion pressure wave reaching the piston exactly at the right moment (TDC) to produce the optimal force on the piston. Factory engines are usually set with the timing somewhere in between these two extremes, so when you play with "advancing" the timing, you're moving it Before Top Dead Center from zero towards the theoretical optimal point.
On most engines you will start to get predetonation (knocking, pinging, etc..) before you reach the optimal spark advance though. This happens since the peak combustion chamber pressure increases as you advance the timing - as the sparkplug fires and the A/F mixture lights off the chamber pressure goes up, but this pressure increase causes the mixture somewhere at the bottom to light off spontaneously. This results in the two flame fronts colliding with themselves and the piston, making the engine internals resonate which we hear as pinging. Enough of this for an extended period will blow a cylinder head gasket or actually superheat and weaken a piston enough to blow a hole right through it.
Going to a higher octane gas makes the A/F mixture less volatile, so it can withstand higher chamber pressures before spontaneously igniting. I'm not an engine designer, but this is all as far as I understand it with a reasonable amount of reading. :?
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