What does Mr. Hyde do?What is the point of having Mr. Hyde?
In the early 20th century, Sigmund Freud announced that all beings have innermost desires that society would not accept. Those desires might be related to gluttony, or violence, or sex, or any number of physical pleasures, but they are wishes that can be harmful to others and that have been repressed since man became civilized (in some more than others).
Dr. Jekyll is a good social man. He has dedicated himself to a life pursuit, and has a strong work ethic. He is an intellectual, and tries always to better himself and the world around him. However, he has found that those "inner desires" of his are getting harder to resist - their call is getting louder, and they are distracting him from his attempt to do good works.
Enter Mr. Hyde. The purpose of this alternate personality is for Jekyll to be able to live out these repressed desires. That is Hyde's purpose, to be the socially "bad" man so that Jekyll can be the "good" man. Hyde is the party animal, if you will, who gets to do what he wants, whether harmful or not. Unfortunately, he begins to take over in the end. Jekyll is brought down because he released these repressed desires.