Not sure what the other posters are trying to say so if I repeat, my bad...
Octane is the temperature at which fuel will ignite. Higher the octane, higher the temp to ignite, hence more compression, hence more power. Our engines run a higher compression so in order to optimize performance you need a high octane fuel. Yes modern engines have knock sensors so when you do have bad gas or lower octane, you won't damage the engine but with that , lower octane can result in less timing to compensate for less compression which will lead to less performance.