It's a torsional suspension element that ties the left and right side of a suspension together. Correct name is ANTI- swaybar... not to be r1c3boi confused with strut tower bars or rather strut tower/chassis bracing.
It acts like a spring between each side of the car so that when you turn the car and it tries to roll and compress the outside suspension unit; the swaybar links that to the inside wheel. Thus to compress the outside suspension, to some degree your car must also compress the inside suspension. Effectively increasing the roll stiffness of the car or the effective spring rate in only the corners.
So when you don't have one, each side of the suspension is independent and you have lots of roll, add a swaybar without too much stiffness and it will give you less roll without lifting your inside wheel off the ground.
Side note: If your car doesn't have factory chassis bracing across your front strut towers or rear towers, it does help if you slap in one from a higher end model or a very solid aftermarket piece. Cheap eGay crap helps a little, but quality pieces are better if they have greater rigidity. It will make your ride feel smoother by taking the shudder out of the body of the car and direct it back into the suspension.