The octane is an indication of the fuel's resistance to be ignited by pressure (also known as dieseling). The higher the compression ratio, the more likely a regular gas will ignite before the spark plug goes off (because of the pressure), so this is why cars with higher compression ratios need to run higher octane gasoline.
If you put a higher octane gasoline in an engine that is rated for less octanes, all you are doing basically is wasting your hard earned money, as the less expensive fuel would work just as well. Other than that, the higher octane will have no other effect.
Anyway, that is what I remember from when I worked for Esso (Exxon Mobile) about 15 years ago! I am sure if I am mistaken in my understanding someone here will correct me...
Felipe