The conflict is that no matter how hard they try to be together the environment around stops them. For instance, the boy cannot go under the sea with the mermaid because it's human. And on the other hand, the mermaid cannot live on the land because it's meant to live under the sea.
Also, people around them are taking away their freedom and stops the boy. They even put him into jail as they thought he was going crazy. By taking freedom away from the boy he forgot the "imagination" and forgot what the mermaid was like. In the end, the boy chooses to go under water. I personally think he did this in order to get his freedom and stay with the mermaid.
The author maybe is trying to tell us that taking freedom away won't make anything peaceful.
