The Strange Case of Dr. Jekyll and Mr. Hyde talks about the duality of human nature. What is Duality? It's a philosophical theory that the world can be divided in two basic entities. In the novel it's good versus evil. As we go through the novel, we realize that humans have both good and evil and one without the other can't exist.
Dr. Jekyll has a socially accepted behavior, but he also wants to do things he has been told all his life not to do. That's why he creates Mr. Hyde, and in a way he releases all his demons. Mr. Hyde takes joy in being evil and doing bad things. But soon Dr. Jekyll realizes that good and bad balance each other, as evil starts to take over.
Basically, the novel talks about the good and evil that exits in every person. We need both to have a balanced life.