How does the Quattro all-wheel drive system in the Audi A3 improve performance?

I am considering purchasing an Audi A3 but I am not sure if the Quattro all-wheel drive system is worth the additional cost. Can someone explain how it works and how it affects the car's performance?

The Quattro all-wheel drive system in the Audi A3 allows for better traction and handling, particularly in difficult weather conditions. It constantly monitors road conditions and distributes power to the wheels accordingly, resulting in a smoother and more confident driving experience.