It really is a waste in most cars.
Gas spontaneously combusts under pressure. Depending on the chemical composition, it combusts under different amounts of pressure.
The most significant thing which affects this is the ratio of Octane to Heptane. More Octane means it only combusts under more pressure.
Car engines compress the gas before igniting it. This can cause a problem since if the gas spontaneously combusts before the spark plug sparks, the cylinder fires at the wrong time. This causes bad efficiency, higher emissions, and can cause engine damage if it is really bad.
There are things you can add to the gasoline to make it bear more pressure before combusting. That is why we talk about an “Octane rating.” The Octane rating is the percentage of Octane which is mimiced in the gasoline by adding additives. That is why you can have an Octane rating over 100.
The best additive is lead, but that has been outlawed. (A few more years of lead and nobody would have been smart enough to outlaw it.)
So, the only purpose of buying higher Octane fuel is if your engine compresses the gas in a way that the lower ones will spontaneously combust. Your owner’s manual will give you this information.
Otherwise, you are just wasting money.