The name "octane" comes from the following fact: When you take crude oil and "crack" it in a refinery, you end up getting hydrocarbon chains of different lengths. These different chain lengths can then be separated from each other and blended to form different fuels. Octane has eight carbons chained together.
The octane rating of gasoline tells you how much the fuel can be compressed before it spontaneously ignites. When gas ignites by compression rather than because of the spark from the spark plug, it causes knocking in the engine. Knocking can damage an engine, so it is not something you want have happening. Lower-octane gas (like "regular" 87-octane gasoline) can handle the least amount of compression before igniting. Likewise, higher-octane gas can handle higher amounts of compression.
The compression ratio of your engine determines the octane rating of the gas you must use. A "high-performance engine" has a higher compression ratio and requires higher-octane fuel.
So, what happens if I run higher octane in my engine if it is not a high compression engine?
There are no real benefits, other than the gasoline manufacturers making more money off of you. When you use a fuel with a higher octane rating than your vehicle requires, you simply send this unburned fuel into the emissions system.
Doesn't higher octane gas have more cleaning additives that are good for my engine?
No. Government regulations require that all gasoline contain basically the same amount of additives to clean the injectors and valves.
In summation, unless your engine is "knocking" you do not need to run a higher octane.
This was written by Charles Fortune, AFM'er of fame, once upon a time.