The title "Everyday Use" is a referent not only to the quilts, but also to one's culture, which in this case is reflected by gender, race, geography, language, values, and vocation.
Mrs. Johnson sees the quilts as constructs of an African-American, matriarchal, agrarian, self-sufficient Southern culture. More specifically, she wants to put the quilts and her culture, race, and language to everyday use to honor the older matriarchs from her family, namely Grandma Dee (who lived during slavery).
If her daughter Dee/Wangero is ashamed to put this extant culture to everyday use, then she dishonors those slaves and the daughters of those slaves during the Jim Crow South. If Dee/Wangero takes her pre-feminist, pre-Civil Rights, agrarian culture for granted and fails to use it every day, then she will be passed over by Mama as the future matriarch of the family. Instead, the honor goes to Maggie who practices the culture daily in her domestic duties and staggered speech.
The story is very much a kind of revisionist Cinderella myth retelling with the domestic servant (Cinderella, or Maggie) being rewarded with the slipper (or quilts), but instead of marriage to a Prince and becoming queen, Maggie becomes the next matriarch (Mama, and then Grandma Dee).
This great story uses the title given to it on a number of different levels, as you have identified. It appears in the story when Dee is protesting that Maggie should not have the quilts that Dee desires so much because she would only put them to "everyday use" rather than hang them up and look at them.
However, key to this story is the conflict between the mother and her two daughters and the way that Dee and Maggie have turned out so differently. Dee is shown to have rejected her poor Afro-American roots in her attempt to embrace her African identity (as characterised by her change of name) and thus it is clear that she cannot appreciate the quilts and the way they represent a real part of her family history. Note what Mama tells us about them:
In both of them were scraps of dresses Grandma Dee had worn fifty and more years ago. Bits and pieces of Grandpa Jarrell's paisley shirts. And one teeny faded blue piece, about the size of a penny matchbox, that was from Great Grandpa Ezra's uniform that he wore in the Civil War.
These quilts then are literally made of pieces of history stitched together. It becomes clear in Mama's choice to give the quilts to Maggie, that Maggie is the daughter who is able to appreciate this and putting them to "everyday use" reflects the kind of family hard-working spirit that characterises their heritage, rather than making it an object to be looked at, as Dee would have it.