How does the Audi A3's Quattro system work?

I'm considering purchasing an Audi A3 and have heard about their Quattro system. Can you explain how it works and if it's worth the additional cost?

The Quattro system, found in all-wheel drive Audi vehicles, uses a center differential to distribute power between the front and rear axles. This allows for improved traction and handling, especially in inclement weather conditions. While it does increase the cost of the vehicle, many Audi owners find the added performance and safety benefits well worth it.