The tree is described in the novel as a continual symbol of growth:
There's a tree that grows in Brooklyn, Some people call it the Tree of Heaven. No matter where its seed falls, it makes a tree which struggles to reach the sky...
Metaphorically, the tree is Francie, & the other characters who struggle to survive in the brutal urban environment. The tree is an anomaly in the "concrete jungle"-one does not see plants, green and vibrant, in such a dreary setting. In much the same way, one may not expect the characters to survive and even thrive in their harsh surroundings. Yet they do, & this struggle is manifested in the growth of the tree. People are like trees-wherever the seeds fall (wherever they're born), they must struggle for life. The fact that the tree is described as reaching to heaven shows the constant attempt of all humans to reach greater heights. We all aspire to "reach heaven" in our own way, much like the tree of the title.
The tree serves as a symbol for the immigrants of Williamsburg. Wherever the tree landed it struggled to reach the sky, just like the Nolans.
It acts as symbolism for the Nolans and other poverty stricken families. The tree's seeds fell to the ground and no matter where they landed it struggled to touch the sky.
francie is the tree and it represents how she struggles to live. it represents hope and escaping poverty