Mrs. Johnson is a mother who has spent her life raising two daughters, trying to give them a sense of where they come from and what is important in life.
Dee is more intelligent and forward-thinking, and she goes off to school and eventually settles in the city to work.
Maggie is not as motivated or pretty as Dee, but she is a good person. She has chosen to stay home, and is now getting ready to marry.
Three generations are presented in this story. Though Grandma Dee is dead, the possession of her quilts comes into question. She is the a woman who represents a source of strength and cultural pride for this family. I think Mrs. Johnson has the same values as she raises her daughters--who both had a relationship with their grandmother before she died.
Dee goes off "to the big city," and tries to leave her "roots" behind her. It's safe to say that her mother is puzzled by Dee's intolerance of her ancestors' history in the United States; this change is evident when Dee chooses an African name and can find no good that has come at the hands of those [whites] who have oppressed her and her people. It's as if Mrs. Johnson doesn't quite know who her daughter has become.
Maggie, on the other hand, has stayed close to home, not just physically but philosophically as well. She is still rooted in the generations that have come before her. She is a proud young woman who seems to be more grounded in the true importance of family. It is easier for Mrs. Johnson to connect to this daughter who has not walled herself away from her heritage.
When Dee announces that she wants the family quilts, made by the hands of previous generations, Mrs. Johnson is surprised (because of Dee's new stance on "family") and now confronted with a dilemma. Maggie had asked to have the quilts.
Dee does not want them for their familial significance, but because they would look nice in her home. Maggie wants them specifically because of the attachment she feels to her family and her heritage through the quilts.
Mrs. Johnson, isn't quite sure what to do. Maggie finally agrees that Dee can have the quilts, stating that she does not need the physical presence of these things in her life to help her feel connected to her family's past, especially Grandma Dee.
As Mrs. Johnson looks at her daughters throughout the debate, she decides that she know which daughter would really find having them meaningful, and so gives them to Maggie.
Mrs. Johnson has raised two daughters, and done well by them. However, the attachment between herself and Dee, and the relationship she has with Maggie, are totally different. Dee can see things only in terms of today, while Maggie keeps one foot in the past, remembering, fondly, the line from which she has "sprung."
Mrs. Johnson will have a closer relationship with Maggie who has not forgotten where she comes from, than with Dee, who wants nothing else but to leave her heritage behind her.
Your question goes to the heart of this short story, and key to understanding what it is trying to say is understanding the relationships between Mama, Maggie and Dee. Consider how Maggie is introduced in the first paragraph:
Maggie will be nervous until after her sister goes: She will stand hopelessly in corners, homely and ashamed of the burn scars down her arms and legs, eyeing her sister with a mixture of envy and awe. She think her sister has held life always in the palm of one hand, that "no" is a word the world never learned to say to her.
This quote clearly establishes some of the central differences between the two sisters. Dee is confident, outgoing, ambitious and determined to make something of life, whereas Maggie is shy, reclusive and passive. Consider how the narrator describes her daughter as a "lame animal" who sidles "up to someone who is ignorant enough to be kind to him". Maggie, described in this fashion, is clearly painted as someone who has such a low sense of self-worth that they are amazed that anyone would actually want to talk to her.
However, the narrator says of Dee, "Hesitation was no part of her nature":
She was determined to stare down any disaster in her efforts... At sixteen she had a style of her own: and knew what style was.
It is clear then that Dee is incredibly self-confident and self-assured. She, as is amply evidenced later in the story, knows what she wants and will not stand for anyone getting in her way, which makes the narrator's decision to not give into her all the more remarkable.
One of the key events in the short story that reveals Mama's character is her refusal to give Dee what she wants, and her insistence that Maggie receives the quilts. It is clear that she loves both of her daughters, but is exasperated by both of them in different ways. However, her decision to give the quilts to Maggie rather than Dee indicates what a high value she places on the family heritage and history, of which the quilts are a symbol. Note too that this is the heritage that Dee has rejected and turned her back on.