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General theory - I'm sure more knowledgable folks will cover it better.
Q: Does timing advance mean the point in the four-stroke cycle where the actual spark occurs, thereby determining how much compression has occured?
A: The timing advance doesn't have any affect on the compression. It is just hte number of degrees before the poston reaches top dead center that the fuel is ignited. You ignite it before top dead center because it does take a certain amount of time to burn, and you want practically all of the burning to be over by the time the cylinder is pushed all the way down and the exhaust valve opens. When the timing is too slow burning gas is released into the exhaust, making it hot and lowering the MPG and power (more of that power is going out the exhaust as heat). Setting the timing too soon, however, allows the gas to burn and reach peak pressure while the piston is still going up, again reducing power and making a pinging or rattling noise. The point at which the spark is fired off needs to change as the engine speeds up - because the fuel still burns at a particular rate, but the piston is moving faster - so the faster it spins the earlier you need to spark it. It also will burn faster or slower depending on the peak pressures - which are related to the compression ratio and the throttle setting, which is why many cars have a vacuum advance. Also, the rate of burn varies depending on the mixture, with rich burning slower, and lean burning faster.
Q: How does the setting determine economy and/or performance?
A: Too fast and the burning fuel buils pressure against the rising piston, so some of the energy goes into slowing it down before it goes over the top and pushes it down. Too slow and the fuel has less time to burn, the peak pressure is less and some burning fuel goes out the exhaust without you extracting any energy from it.
Q: What exactly is "pinging" and detonation?
A: When the fuel ignites too soon or burns too quickly - so that peak pressure occurs before the piston reaches the top of its stroke. Usually makes a pinging or knocking noise.
Q: Is this similar to diesel engines, which do not have a spark plug and simply detonate at a certain amount of compression?
A: Sort of - compressing air heats it up, compress it enough and the fuel will ignite. However, they don't leave the timing of the compression ignition up to chance in a diesel engine, that would be too random and vary depending on barometric pressure, air temp, fuel cetane, etc, etc, etc. Instead, the engine just breathes in a full gulp of air each and every time (idle or wide open 'throttle'), compresses it, and instead of timing a spark the fuel is injected directly into the hot compressed gas, which ignites it immediately (unless you have a worn out old diesel engine that no longer has enough compression, in which case you crank and crank until the battery dies). Some of the very newest gasoline engine technology also uses timed injection of fuel directly into the chamber along with a spark (or several) - which avoids the possibility of pinging or detonation that can occur when the fuel is present during the compression stroke.
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I'm JohnMc, and I approved this message.
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