Basically sway bars accomplish two things. A sway bar is a torsional spring that connects the left wheel on a car to the right wheel. If both wheels move up or down together it imparts no resistance but if the wheels move in contrary motion the sway bar will resist the motion. A larger sway bar will reduce the amount that the car is inclined to lean in a corner and secondly, the balance between the magnitude of the front and rear roll stiffness, a combination of the spring stiffness, shock absorber stiffness and sway bar stiffness, profoundly affects the feel of the car.
Resources:
WWW.AUTO.HOWSTUFFWORKS.COM
WWW.ADDCO.NET
WWW.SUSPENSIONCONNECTION.COM