the difference between regular and premium gas is its octane rating, the yellow number above your pump
when a particular type of gasoline has a higher octane rating, it means it requires a higher activation energy to ignite the gasoline and thusly more compression in the engine, allowing your engine to run more efficiently (although this arguably is more pronounced in vehicles that require a minimum high octane rating)
using a higher octane in a entry-level or generic car will reduce knock and increase performance but the change isn't noticeable if you have been using regular for an extended period of time, especially if your car has a minimum octane rating in the mid-eighties
personally the tradeoff between performance and price isn't worth it in my opinion if you have a non-performance or a car with an entry-level engine, but if your engine is better than most, then it could be worth it to prevent knock
don't see the point if you don't have an engine to utilize it though
wikipedia explains it a little more technically:
http://en.wikipedia.org/wiki/Octane_rating
you can find your car's minimum octane rating in your car's manual