[BrianG]

A sway bar loosely couples the suspension on both sides of the vehicle to help reduce body roll and can be "tuned" by using stiffer bar stock. You don't want it too tightly coupled or when one side articulates over a small bump, the other side will too.

You can see it working by picking up a car (so it's off the tires) with a sway bar setup. Push up on one of the wheels. Once you get to a certain point, the sway bar will cause the other side to raise as well, just not as much.