What does the narrator mean when said,"Alive, Miss Emily had been a tradition, a duty, a sort of hereditary obligation upon the town"?
It was typical in Southern society to take care of the old, sick, or otherwise needy people. Every town has the recluse or the eccentric that the town just overlooks and accepts. It is the Southern way to accept our own and take care of our own problems. In To Kill A Mockingbird, you have Boo Radley who the town accepts as part of their society. Southern literature just captures the reality of those aspects of Southern culture. Miss Emily comes from a once well-to-do family and her status is revered even though she may be talked about as eccentric.
Emily's family was entrenched in a socially prominent position. Emily was awarded special privileges based upon her father's achievements, not her own. While she was not loved, or cherished, it was accepted in the town that she was special. She was an obligation that the town had no choice to defer to, protect, and revere. Because it was done since the time of herfather, it was natural to continue the special treatment.
Emily is the daughter of a famous war veteran. Because of his service, his family was granted special privledges, like not paying taxes, that continued to benefit Emily even after her father's passing. The special treatment did not endear her to the town's people. They looked at Emily, as Faulkner describes, as an "obligation" that was burdernsome at worst, annoying at best.