2009 Lexus ES 350 Premium Gas

Yes. Octane is a chemical that is added to gas to make it less explosive. The reason for this when the piston inside of your engine compresses the fuel air mixture, it can explode before the spark plug fires. If this happens, the piston will fire down the cylinder wall before the crank shaft and the piston rod reach their piviot points. If this happens you will hear a "ping" or a "spark knock". This (in time) will destroy an engine.
The higher the octane rating the less explosive the fuel and the higher the compression can be in the engine - thus more horse power. The lower is just the opposite.