Basically it improves handling in corners.
Here's some info I found online that may help:
Strut Braces
If you're serious about your car's handling performance, you will first be looking at lowering the suspension. In most cases, unless you're a complete petrolhead, this will be more than adequate. However, if you are a keen driver, you will be able to get far better handling out of your car by fitting a couple of other accessories to it. The first thing you should look at is a strut brace. When you corner, the whole car's chassis is twisting slightly. In the front (and perhaps at the back, but not so often) the suspension pillars will be moving relative to each other because there's no direct physical link between them. They are connected via the car body, which can flex depending on its stiffness. A strut brace bolts across the top of the engine to the tops of the two suspension posts and makes that direct physical contact. The result is that the whole front suspension setup becomes a lot more rigid and there will be virtually no movement relative to each side. In effect, you're adding the fourth side to the open box created by the subframe and the two suspension pillars.
