It goes like this: premium gas is more stable (i.e., less likely to spontaneously ignite, especially under pressure) than lower fuel grades. This is because it has a higher octane rating, or specifically, its composed of a higher ratio of stable octane vs. unstable heptane. The bottom line? The higher the compression ratio of your engine–in other words, the more your engine compresses the fuel/air mixture before combustion–the riskier a lower octane fuel will be since heptane gets more unstable under pressure. By “risk,” I’m referring to the risk of engine knock, which is when fuel spontaneously ignites at the wrong time in the engine cycle.
If your premium-requiring vehicle runs fine on regular, fine. Lucky you. If you’re less lucky, however, using lower-grade fuel can mean a bunch of knock, especially when certain cars are driven in anger. A turbocharged car’s compression increases proportionally to the amount of exhaust generated, meaning that driven very aggressively, you’re more likely to experience knock than if you’re just puddling around. My car, for instance, is not only turbocharged (a mechanism for increasing compression), but I can increase the boost pressure on the fly. At stock setting, I actually do occasionally get a nice backfire with lower grades of fuel (though it’s not common). At severely increased boost pressure, on the other hand, I actually need higher-than-premium. I don’t ever use that except for the occasional lapping (track) day.