This is really no different than a manager providing feedback to their direct reports. If you want people to listen and even accept advice, they must believe that you (1) want to help them and (2) are able to help them. A strong board increases a CEOs perspective. This is extremely important since CEOs often get a limited view of reality from their direct reports. By creating a constructively challenging partnership, the board can create a much broader viewpoint which improves decision making and should increase stockholder value.