The significance of a fence in this play is that it serves a dual purpose -it keeps people in and it also keeps them out, both literally and figuratively.
The most obvious fence is the literal fence that is being built throughout the play. A physical fence implies ownership (and this play can be viewed as the African American version of the American Dream theme of home ownership). Building a fence around your home is a way to claim it as yours by determining who can and cannot leave.
For Troy, there is a figurative fence that keeps him stifled at work. He asks the question of why the blacks are always lifting the trash while the whites are driving the trucks. He sees this as a fence created by the white majority to keep the black minority in their place socio-economically.
Another fence is the fence that kept Troy in place during his time in prison. In this case, the walls kept him inside. When he builds a fence around his own home, he is able to keep his family inside (not literally, but it acts as a barrier between his family and the dangers of the world around him).
Finally, the characters build fences between each other. Troy and Rose have a fence between them from the standpoint of gender difference. Troy cannot express to Rose the same emotions he can express to Alberta. This is one example of fences built between people. Another lies in the Troy and Cory dichotomy. Troy tries to fence Cory in by keeping him from pursuing his dreams because he believes that Cory will fail and wants to protect him from that.
Each character has a fence of some sort that he or she has created either to keep others out or to lock himself or herself inside. Gabriel is the only exception. The simplicity of his beliefs, while flawed from the perspective of "normal" society, actually allow him to transcend self and societally imposed fences.