What is the purpose of the Audi A3's auto start-stop system?

I've heard the term "auto start-stop system" mentioned when talking about the Audi A3. What does this system do and how does it work?

The Audi A3's auto start-stop system is designed to reduce fuel consumption and emissions by automatically shutting off the engine when the vehicle is stopped, such as at a red light or in traffic. It then restarts the engine as soon as you release the brake pedal.