Thanks to Grape Ape Racing for providing some good information.
Octane
Octane is a rating of a fuels resistance to ignite. The higher the octane, the harder it is to get to ignite. A higher octane may be necessary to prevent pre-ignition and detonation in a high performance engine. Higher octane fuel will generally burn slightly slower than a lower octane fuel which could require a change in ignition timing. Using more octane than you need will not help power, the slower burn rate will actually cause you to lose some power.
Detonation
Normal combustion will take place at a pretty steady rate (for a given rpm and load), when a large amount of the charge burns extremely fast and uncontrollably, it is know as detonation. Detonation can destroy an engine in a matter of seconds. It is common knowledge that heat causes detonation, but heat it not the only cause. Pressure plays a big role in it also. You can get detonation by running with too much ignition advance, if heat was the only cause, signs of detonation would around the exhaust valve, but this is not the case. Usually when detonation takes place from too much advance, the detonation occurs on the intake side of the chamber, which is the coolest side of the chamber. This happens because detonation did not occur until the pressure got excessive, which was after the spark. By the time that happened, the charge near the exhaust valve has already been burned. Most of the time, detonation will occur after normal combustion has started. Apart for destroying pistons and spark plugs, light detonation can cause all sorts of other problems, like fatiguing cranks and rods quickly and pounding bearings to death, so avoid detonation at all costs.
Pre-Ignition
When the charge lights off before the spark, it's called pre-ignition. This can happen with or without detonation, but usually will cause detonation in a high performance engine. Hot spots in the combustion chamber are the usual cause of pre-ignition. A spark plug with a high heat range can cause a hot spot. When pre-ignition occurs, the charge begins to burn, then when the spark plug sparks there are two flame fronts. This is very unpredictable and can lead to detonation, because it will act just like too much ignition timing, but it wont be controllable.
Motor Octane Rating
The motor octane rating, referred to as MON (motor octane number), is the best rating to use when selecting fuel for your race or high compression engine. When testing MON, the fuel is heated to 300° F and the intake air is heated to 100° F. The test engine is a single cylinder 4 cycle engine that is run at 900 rpm. Ignition timing is varied with compression ratio. Engine load is varied during test.
Research Octane Rating
Known as RON (research octane rating). Tested at 600 rpm with a fixed timing of 13° BTDC. The fuel temp is not controlled at all and the intake air temp is varied with barometric pressure. This is done to covert everything to a SAE standard day, which is 60° F, 0% Humidity, and 29.92 inches barometric pressure. The RON should not be used when selecting fuel for a race or high performance engine. The RON will always be higher than the MON.
(R+M)/2 Rating
This is what you get at the gas pumps. It is average of the RON and MON. It is ok to use this for lower compression street motors, but when you get much over 10:1, you should really pay attention to the MON. The closer the RON is to the MON, the more stable the fuel is. This can be very critical when running 7000+ rpm.
Specific Gravity
This is the weight of the fuel compared to water. If a race fuel has a .75 Specific Gravity (or SG) it is 3/4 of the weight of the same amount of water at the same temperature. Fuel with lower specific gravity will have a higher BTU content when burned and be more stable at high rpm's. A lower specific gravity also makes jetting more critical because the engine will run leaner (less dense fuel). A fuel with a higher SG will run cooler (if no jetting changes have been made to compensate), because a denser fuel will make a richer mixture. A fuel air mixture is not measured in volume, it's measured in weight. For a 12:1 mixture, you have 12kg. of air to 1kg. of fuel.