There is a tree called the Tree of Heaven that grows ironically in Brooklyn, as the title suggests. An interested way to interpret this beautiful story would be to take each character and reconcile them to that basic imagery. As an image, the tree suggests the idea of hope, because in the city, everyone desperately wants (and needs) more trees, and this is never more true than in low-income areas where developers tend to remove all trees. So, a tree growing in the tenement yard is a reminder of life's persistence, and that's exactly what all the best characters of the novel demonstrate.
The first tree character is Katie. Katie sees Johnny on a date with another girl, and she makes a deal with God. She promises never to complain about their fate together, if only God will let her be with him. Then later, when Johnny turns out to be a dud who just gets drunk every day, she makes good on her promise to God, getting up to start supporting the family herself, supporting them as a janitor. This makes her a symbol for hope in the eyes of Francie, her daughter. She represents life. Johnny on the other hand, represents death, because he literally dies in a drinking stupor, but also because he has deathly, dangerous habits.
In the end, the family discovers that although Johnny's indiscretion was a serious roadblock for the family, it doesn't mean that they have no hope. Like the tree that grows as a sign of life and nature in a place made of concrete and bricks, the family's hope comes from the persistence of the characters, and ultimately, they are rewarded with a life of abundance and provision when the Sergeant marries Francie's mother, sending her off to the University of Michigan. Compare that gift to Johnny's gift of death, despair, and hopelessness, and the novel comes into focus.
