The conflict in Robert Louis Stevenson's Gothic novel Dr. Jekyll and Mr. Hyde is the struggle between Dr. Henry Jekyll and the dual nature of his personality. As a Victorian, Dr. Jekyll enjoys the reputation and recognition of the best social sets. He is known as a man of prudence and intelligence, which is what earns the respect that he gets from his upper-class peers.
Yet, it is quite obvious that there is a dark side that Henry Jekyll wishes to experience, and he does not openly attempt to do it because of his fear of breaking the iron-clad rules of decorum that dominate the overall psyche of the Victorian society where he lives.
To be able to indulge in the pleasures of sin and innate secret desires, Jekyll abides by his Promethean nature of desiring to change the natural order of things and creates a way to transform himself into another man: Mr. Edward Hyde; one who does as he pleases and responds only to his own wants and operates under his basic Id.
Hence, the conflict: In wanting so badly to protect the outer image of Dr. Jekyll, and also in wanting so badly to indulge in the sins of Mr. Hyde, Henry Jekyll does not take into consideration that both personalities would still need to be under control. Mr. Edward Hyde is never controlled, and is left to act as badly as he wants. It is this freedom that grants Hyde the power and the strengths that make him so much stronger than Dr. Jekyll. Conclusively, Hyde's inherent and sinful nature (perhaps ALL of our natures, as well?) is much more powerful than the monitored and well-manicured persona of Dr. Jekyll that the world sees.
The resolution begins when Hyde starts taking over and dominating the persona of the man. Hence, whenever Jekyll is able to go back to being himself, he immediately locks himself in his lab. The experiment of the dual personality has gone completely awry and, from what the reader learns, the man kills himself...under the personality of Hyde. We learn about the resolution through Lanyon's letters which also represent one of the most climactic moments of the novel.