of the rest of the sentence. Falkner writes,

Alive, Miss Emily had been a tradition, a duty, and a care; a sort of hereditary obligation upon the town, dating from that day in 1894 when Colonel Sartoris, the mayor--he who fathered the edict that no Negro woman should appear on the streets without an apron-remitted her taxes, the dispensation dating from the death of her father on into perpetuity. (1)

The information in between the em dashes gives the audience background knowledge about Colonel Sartoris. Apparently, Colonel Sartoris issued an edict stating that no African American woman should appear in public without an apron. This information is significant and emphasizes that Colonel Sartoris is a figure from the Old South. Such an edict seems backward and questionable by the newer generation of southerners. However, Colonel Sartoris was a traditional man, who subscribed to Antebellum Era culture and laws, which included extremely prejudiced views towards African Americans.

Miss Emily Grierson hails from a prestigious, aristocratic southern family and is described as being a "tradition, a duty, and a care" to the town of Jefferson. Following the death of her father, the town's mayor, Colonel Sartoris, remits Emily's taxes "into perpetuity." Essentially, Colonel Sartoris cancels Emily's taxes for an infinite amount of time. The word remitted means to cancel while the word perpetuity means forever. Therefore, Emily Grierson is no longer required to pay her taxes in the town of Jefferson for as long as she lives.

Colonel Sartoris symbolically represents the Old South and remits Emily's taxes as a way to offer her financial aid and assistance after her father passed away. Knowing that Miss Emily would never accept charity, Sartoris fabricates a story about her father loaning the town money and claiming that remitting her taxes was Jefferson's way of repaying the Grierson family for the favor. Towards the beginning of the short story, the newer generation of aldermen visit Emily's home in hopes of persuading her to pay her past due taxes.

If you are referring to the phrase from A Rose for Emily, it just means that Emily was sparred any obligation to pay her property taxes from the date of her father's death until eternity.

The word 'remitted' means cancelled, and the word 'perpetuity' refers to a lasting or eternal state. In the story, the author states that Emily was a 'tradition, a duty, and a care; a sort of hereditary obligation upon the town,...' when she was alive. Accordingly, in 1894, Colonel Sartoris, then the mayor of the town, coined a story about the largesse of Emily's father in order to spare Emily a financial burden.

Supposedly Emily's father had loaned some money to the town, and Emily's tax remittance was a way of paying her family back for their generosity. However, this was a fabricated story, concocted for the sole purpose of financially aiding Emily, a woman who was too proud to accept charity.