How does the Audi A4's quattro system improve driving performance?

I've been considering purchasing an Audi A4, but I'm not sure if the quattro all-wheel drive system is worth the extra cost. Can someone explain how it works and what benefits it provides?

The quattro system in the Audi A4 uses a center differential and torque vectoring technology to constantly monitor and adjust power distribution between the front and rear wheels, providing enhanced traction and control in all driving conditions.

In addition to improved performance, the quattro system also increases driving safety by reducing the risk of wheel spin and skidding on wet or slippery roads.