Gentlemen and Ladies,
My Father was an engineer at Exxon for 33 years before he retired. Here is some of the fuel wisdom he relayed to me over the years…
The previously mentioned characteristic of "octane" referring to resistance to detonation is correct. Will higher octane gas give you more HP and fuel economy? No and Yes. In an engine designed for 87 octane, using a higher value will yeild NO, nada, zip, the-goose-egg, bupkus increase in HP or mileage, in fact, it may even reduce it. However, if your engine's computer is "tuned" for the additional octane (typically by advancing the spark) then the higher octane will give a bit more power. Also, if you go and retune your car to utilize the additional octane, you can't put 87 in it again without risking detonation (knocking/pinging).
As mentioned, the pump octane rating is the average of the RON (research octane number) and MON (motor octane number). The RON number is significantly higher than the MON due to the testing conditions. The RON is determined while running the engine at constant speed and low engine load. The MON is determined at high rpms and high load conditions. Thus, the MON is more indicative of the engine's requirements during hard/spirited driving (like racing).
Also note; there is no way to know what the individual values are. For example … an octane rating of 90 on the pump could have a RON/MON of 92/88 or 95/85. I would rather have the 92/88 stuff in my car since the MON value is greater. Detonation will usually occur under "MON-like" operating conditions (fast acceleration and high load) so the 88 MON stuff is better. Unfortunately, the 95/85 stuff is probably cheaper to make so this is what they'll sell.
The take home message here is to use what the manufacturer specifies, they tend to know a lot about the engines they make (who would have guessed?)