Well, according to Freud, he argued that our internal consciousness was made up of three elements: our selfish side that tried to get us to act in a way that would enable us to achieve our instant desires (the ego), a restraining force that acted as a check on the ego (the id), and then finally a kind of overarching element that acted as a judge between the id and the ego (the superego).
If we examine this classic tale of split identity, we can see that what happens is that a man who is normally able to keep himself in check through his superego concocts a potion that gives his ego free range over his consciousness and overpowers his id and superego. If we look at the final chapter, the account of Henry Jekyll of his own story, we can see that he has realised that mankind is made of two parts at least, and the first time he takes his concoction, note how he describes the supremacy of the ego:
I knew myself, at the first breath of this new life, to be more wicked, tenfold more wicked, sold a slave to my original evil; and the thought, in that moment, braced and delighted me like wine.
The reference to increased wickedness clearly establishes the way in which the power of the id has vanished, as is also suggested by the drop in physical stature of Mr. Hyde. The point of the story is, in psychoanalytical terms, that Dr. Jekyll manages to find a way to make his ego so dominant that it completely overpowers his superego and id.