KenG's description is accurate. A fuel's anti-knock characteristics are measured and assigned a number that represents how those characteristics compare to a mixture of iso-octane and heptane. Fuel rated at 87 has a resistance to preignition similar to a mixture of 87% iso-octane and 13% heptane. This is a simplification and there's more to it than that, as there are two generally accepted measures of anti-knock which return different results depending on the test. But this is a good layman's way of understanding the idea.

100% ethanol is more knock-resistant than 100% iso-octane, which is why E85 has a rating higher than 100.

For fuel economy, note that that fuels with high octane ratings contain LESS ENERGY than lower rated fuels. Engines burning high octane fuel compensate for this lack of energy by burning more fuel. For example, when the computer in your flex fuel vehicle reads that you're running E85 it just pumps more fuel in to make up for it. Hence the consistently lower mileage when running E85.

Specifically talking about E85: It has about 1/3 less energy than gasoline and at least 1/4 less than E10. That's why you must burn 25%-35% more to drive the same distance. And that's why E85 must cost at least 25% less than gas to break even on it, notwithstanding the feel-good factor of running it. Speaking strictly economically, gas at $2.80 per gallon requires E85 at less than $2.10 per gallon to make sense in a flex fuel setup.

It's actually pretty easy to decide what to run. In Brazil where everything is E85 and they make ethanol from sugar cane, drivers all know how to tell what to buy. When they get to a station, if E85 is 2/3 the price of gas or lower, they buy E85. As soon as it goes higher than that, they know the mileage drop will offset any savings and they switch to gas for the better fuel mileage. It's remarkable how they have adapted.

RE: The original question: When it comes to commercially available motor fuel, energy content drops as octane rating rises. The higher the rating, the "weaker" the fuel. Choosing a higher octane fuel like E85 or premium gas at the pump will almost almost always decrease, not increase, fuel mileage.

YMMV, but that's how it works in a fixed setting.