How is the relationship between Dr. Jekyll and Mr. Hyde important to the theme of duality?
The relationship between Jekyll and Hyde is essential to developing the theme of duality in this work. There are several reasons for this.
First, there is the core relationship. These men change into one another. They are one another's secret identity, in a way. When one man is present, the other doesn't exist.
Jekyll indicates other, deeper elements of their relationship in the work's final chapter. In that chapter Jekyll says that he's always had a divided self, and that through his research he has found that human nature is innately divided: we all have two selves, at least. (In that final chapter, Jekyll says there might be more selves.) So, the relationship between Jekyll and Hyde stands in for the duality in all mankind.
Another element is that the line between the two of them is not firm. It leaks. To be specific, Jekyll thinks he's been successful at dividing himself in two in a way that gives him complete control. He hasn't. At times he goes to sleep as Jekyll and wakes up as Hyde. This indicates that any duality is not absolute: what people repress or deny always comes back.