Well simon, it makes the steering wheel perform like the real thing.
For example, if you had it unchecked, your wheel would be loose all the time, and you wouldn't have any resistance from the steering wheel if you slid or anything. It would just be loose and you wouldn't feel the car's steering tension come into play.
Because, if you try and do a test with the wheel, always do a 360 in your car and let go of the wheel. Just like a car's wheel would really act, it would spin freely and try to countersteer on its own. When you have the option unchecked, it would not do this, and it can result in some unpredictable driving. If you have it checked, but at 0%, it is the most realistic, creating the right amount of looseness and self-countersteering. And if you wanted to tighten up the strength, you just increase the Force Feedback in the game or in the controller's properties. If you increased the centering strength to some percentage (say 50%) for example, the steering would just want to stay centered and not spin freely for the best control.
It is a very important setting if you want to be in full control of the car, and feel more of the car when in a slide or whatnot