The Sway bar's main function underneath the car is to reduce body roll. It does this by connecting both the left and right sides of the car and suspension to the chassis using the sway bar. When under hard cornering, the car rolls to one side which will twist the sway bar. The different ways of how a sway bar is composed will effect the amount of resistance it will have to this twist. Less twist means less body roll. To achieve less twist you upgrade your sway bar. Front and Rear sway bars have a great affect on under steer and over steer. Many times, a stiffer rear bar will net more over steer while a stiffer front bar will net more under steer.
This is Cusco's 16mm Hollow Sway Bar for the Rear of the BRZ/FR-S and 168% stiffer than the stock sway bar.