When you gain a Director Level, you will gain one skill point. Skill Points can be spent on special abilities called Director Skills that allow you to customize your own personal strengths as a director. Think of it as a way to further personalize your style of play.
Some Director Skills cost more than one skill point, and some require a certain Director Level to attain. All of this information can be seen by clicking the "spend" link next to your group's skill points on the Director Overview page.