Brighton Beach Memoirs is a coming-of-age story, meaning that it shows how the main character makes a transition from childhood to adulthood.  Eugene is almost 15-years-old, and he is starting to experience puberty.  Although the wet dream shows that his body is changing, he is not emotionally ready to give up childhood just yet.  For example, while he resents having to go to the store for his mother, he is still dependent on his parents for room and board.

Eugene is not intellectually ready for adulthood yet either.  He is still in school and is in many ways very naive.  This is why he constantly asks his older brother for information about sex and girls.

By the end of the second act, Eugene has matured a lot.  He realizes that his adolescent worries are very small in relation to the family's problems as a whole.  He is now ready to confront the changes that are occurring in his body, his mind and his life.