Sway-bar, anti-sway bar, or anti-roll bar for us older folks.
It's a bar which connects each side of the suspension to the other. It acts as a torsion rod, so turning one side relative to the other exerts force on the less-loaded wheel. IOW, if you're making a hard left-hand turn, the bar is rotated "up", and wants to push the left wheel up with it. Because of spring resistance, this force is difficult to exert, resulting in the body of the car leaning less relative to the wheels. Hence, you're 'stabilized'. Not as much 'body roll'.