There are various types of success in life and a portion of that multitude is reflected in this play. Relationships, careers, and the attainment of maturity are each areas explored in the play, achieved with varying degrees of success (and failure).
For Rose, a stable family life is all that is desired for success. This notion literally defines her character in the play, as she is introduced with an author's note to this effect. As long as Troy remains faithful and the family life continues uninterrupted, Rose is successful. This does not mean that the family life has to run smoothly. Nor does it mean that relationships within the family must be open or strong.
Rose wants the fence built around their house so that she can keep her family safe within its confines.
Troy destroys Rose's chance at a successful marriage and family life when he announces that his mistress is pregnant. It is Troy who defeats Cory's chance at early success as well. Cory has a chance to go to college on a football scholarship.
But Troy is so bitter over his own lack of opportunity that he holds his son back from any success he might achieve.
Throughout the play, Troy tells and retells the story of his baseball career with bitterness. This particular narrative element presents what can be taken as the play's overall commentary on success.
Troy had a great baseball career, yet he never made it to the major leagues. His friend and his wife tell Troy that he should be proud of his achievement and that his career was successful. Troy, however, can only see his career as a failure because he did not get to the major leagues.
The failure that Troy clings to with such bitterness is open to interpretation and can be seen as a matter of perspective. This applies to his marriage as well. Troy cheats on Rose, not because there are problems in the marriage, but because he feels that there is something he can get outside of the marriage that is unavailable in it.
This too is a matter of perspective, as Rose points out. Professionally, for Troy, the same importance of perspective applies.
He has noticed that only white men are promoted to driver, and, although he possesses no driver's license, Troy complains about the injustice of a system that favors one race while excluding another.
Achieving the promotion he agitated for, Troy remains unhappy with his job. Having a functional marriage, Troy chooses to go outside of it to find happiness. Having had a renowned baseball career, Troy fixates on the one thing he did not achieve.
This character flaw in Troy effectively generates all of his failures. Success is available to Troy. No fence is keeping him from being happy. Though he proves himself to be powerless to alter his perspective, Troy is ultimately responsible for his failure and success.