Stiffer rear sway bar lends to less body roll. This allows effecient weight transfer and less "pushing" in the corners meaning more steering responce. The simple answer is - you can enter the corners faster and turn harder.
Understeering happens when you are turning into a corner and the weight transfers in such a manner that the car pushes around the corner. This mean the car is sliding forward while it is also turning. Example- you are turning the wheel 50% to the right at 40mph and your car is really only turning 40% b/c its pushing 10% due to the above noted events. There are alot of other things someone can do to get closer to 1:1 like camber, toe and tires but we dont really have all that in the factory set up..... So, the next best thing outside of $2000 tires and even more in sport suspension upgrades is, the rear sway bar. Some people also do the front strut tower brace and front sway bar as well. However, if youre not road racing the ST, this is overkill and not needed. you can do the strut brace if you really want but there are mixed reviews on the true impact to the drive.
I came from an Audi S4 with mag-ride sport suspension and an upgraded rear sway bar. When I got my ST I thought i was going to roll it just getting on the highway LOL. The first thing i did that week was install a Steeda rear saw bar and It makes a HUGE difference in the handling!