In William Faulkner's short story, "A Rose for Emily," the entire quote is:
Thus she passed from generation to generation—dear, inescapable, impervious, tranquil, and perverse.
This comment describes Miss Emily Grierson. She is dear in that she is a remnant of days when the Old South was a noble place—not completely ruined yet by the effects of the Civil War.
‘‘A Rose for Emily’’...covers approximately three-quarters of a century. The birth of Emily Grierson takes place sometime around the Civil War. Her death takes place sometime in the late 1920s or early 1930s...
This would have been a time when Miss Emily would have seen many changes, from the devastation of post-Civil War life to the final insult to an already-suffering South: the Great Depression of 1929, which lasted through the 1930s—further oppressing a portion of the country still trying to rebuild after the destruction of the Civil War physically (in terms of the farm land and houses) and economically.
"Passing from generation to generation" describes the amount of time over which the story takes place, describing Emily's life as her father's daughter—living under his control—and then moving about freely (and outrageously, many women thought) after her father died. The movement of one generation to another is also felt in the old ruling by Colonel Sartoris that freed Miss Emily from paying taxes...remitting her taxes...
...the dispensation dating from the death of her father on into perpetuity.
The fact that later generations were unable to get her to pay her taxes after the death of Colonel Sartoris might well make the men believe she was "inescapable." Unrelenting, she refused to budge an inch from the agreement made about paying out taxes.
The passing of the generations is also felt with regard to Miss Emily, at one time, providing china-painting lessons to the children in the community until it fell out of fashion.
...her front door remained closed, save for a period of six or seven years, when she was about forty, during which she gave lessons in china-painting. She fitted up a studio in one of the downstairs rooms, where the daughters and granddaughters of Colonel Sartoris' contemporaries were sent to her with the same regularity and in the same spirit that they were sent to church on Sundays...
The term "impervious" is defined at Dictionary.com as:
...incapable of being influenced, persuaded, or affected
This is certainly the case with Miss Emily. No one can convince her to behave in a "genteel" way with Homer Barron, neither will she be moved by continued pleas for tax monies. "Tranquil" also describes Miss Emily. She does not stand up against her peers and explain herself—she sees no need. She goes about her business seemingly without a care. She is calm, too, when the Board of Aldermen comes to try to collect taxes. She does not yell or argue. She is immovable.
Perverse is defined as:
...turned away from or rejecting what is right, good, or proper; wicked or corrupt.
Emily is perverse
in that she rejects the mores of society: she goes out riding publicly with a Yankee, and a blue collar worker—at that. She obviously carries on a physical relationship with Barron, another socially-corrupt behavior.
The adjectives provided describe someone the town cares about to some extent; but she is not a woman to be controlled: Miss Emily is very independent and comfortable (it seems) with the choices she makes.