The grandmother's hat is the primary symbol in Flannery O'Connor's short story, "A Good Man is Hard to Find." The hat is a symbol of the grandmother's moral code, which eventually turns out to be wrongheaded once the plot makes its final turn.
As the grandmother gets ready to take a trip in the car with her family, she puts on clothes that would let people know that she had been a lady, in the event a fatal car accident ruins the trip. The fact that she's so concerned about the way she would look after death shows that her priorities are out of kilter. Rather than showing concern about the fact that her grandchildren also likely would have died, she is most concerned about the way she would appear.
The grandmother's concern about maintaining her status as a Southern lady shows her to be egotistical, with questionable moral precepts. When a car accident does happen, the hat falls apart, showing the frivolity of grandmother's moral ideas. Once she flies out of the car and the Misfit confronts the family, the brim of her hat drops off. The fact that the grandmother sheds her ruined hat shows that her self-conception has been destroyed as well.