This question refers to the events portrayed in Chapter 16, which describe the author's first experience of work when she goes and helps in a white household, cooking and cleaning. After she has been called "Mary" by her white employer, she realises that she cannot stay there, as she refuses to be "called out of her name" and to allow a white person to shape her identity by giving her a different name. However, at the same time, she is very aware that her grandmother got her this job and therefore she will be unable to simply quit because her grandmother will not let her without a good enough reason. After some discussion with her brother, Bailey, the author decides to break some of her employer's most precious china, so that she can be fired. Note what the reaction is when she does this:
I could never absolutely describe to Bailey what happened next, because each time I got to the part where she fell on the floor and screwed up her ugly face to cry, we burst out laughing. She actually wobbled around on the floor and picked up shards of the cups and cried, "Oh Momma. Oh, dear Gawd. It's Momma's china from Virginia. Oh, Momma, I sorry."
Magaret therefore hopes to get fired by this act, and she certainly achieved what she wanted, as the somewhat emotional response from her employer demonstrates. She manages to be free of being shaped by whites, and keeps her name through this act of independence.