The main concern of Walker's "Everyday Use" is the understanding that the three women of the family have about their traditions and culture. For the narrator this understanding involves matriarchal ancestry. Dee, for instance, is named after her sister and her sister (Auntie Dee) was named after their mother (Big Dee). Likewise, the quilts, a metaphor of the women of each generation, are also symbolic of the strength found in connecting with one's roots that is sometimes in conflict with progress.
When Dee went to college, the mother offered her a quilt, but she refused to take such an old thing. Now, absorbed in her new Nationalist Movement, Dee/Wangero desires the quilts simply for their aesthetic merit, not because of any relational ties. The mother gives the quilts to Maggie, who has been taught to quilt and who appreciates the history of the squares from her Great Grandpa Ezra's uniform and pieces of dresses belonging to Grandma--stitching that was all done by hand.
When Dee says, "Maggie can't appreciate these quilts!...She'd probably be backward enough to put them to everyday use," Mama makes the decision to drop them into Maggie's lap in an act of love, saying "I reckon she would....I hope she will!" For, that is exactly for what the quilts are meant: an "everyday use" reminder of an ancestry of motherly love.