To add to the previous answer for this question, there is a really poignant scene in the play that points directly to the importance of the title. In Act Two, Scene One, the story is well established as a conflict between Troy and his inner demons as well as a conflict between Troy and his family members. Cory, his son, and Rose, his wife, have different expectations of him than he has of himself, and vice versa. This scene in Act Two reveals some of those misunderstood expectations, and it reveals how the fence stands as a symbol for the type of love and relationships the family members value, particularly Rose, who asked Troy and Cory to build the fence.
In this scene, Bono, Troy's friend from work, is visiting as he usually does, and Cory is helping Troy cut the wood for the fence. Cory comments that he doesn't understand why his mother wants a fence built anyway, and Troy agrees that he doesn't understand, since they don't own many valuable things that people would want to steal. To this, Bono responds:
"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. She loves you."
Rose's role in the family is the role of peacemaker and caretaker, so this idea of the fence symbolizing an embrace, a surrounding mother's arms, is relevant to her character. Ultimately, the fact that the fence takes so long to build and is unfinished for most of the play contributes to the idea that Troy and Cory will not be kept. Troy will cheat and die before long, and Cory will join the military and move away. The fence, which was meant to pull everyone together, will serve more as a catalyst for their parting and as a shell for Rose and baby Raynell to retreat into once they are left alone.