To start answering this question, think about the way fences function as symbols in this play. First, why do different members of Troy's family want to build a fence? As Bono says in Act II, "Some people build fences to keep people out...and other people build fences to keep people in. Rose wants to hold on to you all." Rose, Troy's wife, wants to build a fence to keep her family safe and protected, much as she sees Jesus as a fence and protector. Troy, on the other hand, wants to build a fence to keep death out after Alberta, the mother of his baby, dies in childbirth.
As much as fences can offer protection, fences can also keep people out. Think about the larger meaning of fences in Troy's life. He has been kept out of playing baseball in the white leagues because he is African-American. He won't let his son, Cory, play football because he is afraid of racism, and, as a result, Cory decides to leave home. The fences, or ways that Troy has been left out of parts of American life because of racism, cause there to be fences, or divisions, in his own family. In considering the answer to this question, think about the ways in which fences keep people in but also keep people out.