The conflict in this story is man vs. self. Jess struggles with himself because he feels out of place in home dominated by woman. He feels out of place because his passion - art - is not understood by his father or his peers. Jess feels at odds with the world around him and doesn't know how to be true to himself but also fit in.
Meeting and becoming friends with Leslie allows Jess to find a place with himself. In their friendship, and in the world that they create, Jess is able to express himself and to feel accepted. This allows him to understand that he doesn't have to "fit in" to achieve happiness. Instead, he needs to accept that being different is ok, and being true to himself is what will allow him to be happy. Sadly, it is Leslie's death that allows Jess this finally realization that who he is as a person is acceptable - he is able to express grief to his father and is comforted by him.