The title refers to the quilts but more metaphorically, to the basic conflict in the story.
Literally, the phrase "everyday use" refers to the way in which the mother wants the quilts to be used. She sees the quilts as useful objects, rather than as heirlooms to be hung up and looked at.
The title also refers to the general conflict that is going on in the story. It refers to the conflict between the old-fashioned "everyday" type of people like the mother and people like Wangero who has all these new ideas. The everyday people are down to earth and practical, the others are more interested in ideas and philosophical statements.
The significance of the title Everyday Use is that things that are treasured and passed down form generation to generation are meant for Everyday Use and not to be displayed as a trophy. Using cherished items keeps the memories and the past alive. It brings us the warm and loving feelings that make us cherish the items so much. To wrap yourself up in one of those quilts would let you drift back to earlier times and actually picture Grandma quilting and seeing all the time and love that went into making these priceless items. To just display them seems cold and so withdrawn from your past. Dee didn't want to be a part of her past she wanted and still wants the "good" life. Maggie is living the day to day memories of her past because she has grown up respecting it all her life, even with the hardships and devastations she has had to endure. Living, breathing and respecting your culture is taking the good with the bad.
The phrase "everyday use" crystallizes the conflict in the story and governs the structure. As the action develops we see the contrasting values of the two sisters. Dee rejects the past and is creating a new identity for herself. Maggie simply takes the past for granted and also accepts her role in the movement from past to present to future. These two movements of values intersect at the quilt and what is to be done with it. Should it be hung on a wall for display, or should it be put to "everyday use"? Though the story exposes Dee’s pretentiousness, it would seem to be suggesting a compromise. The African-American heritage is alive and present; creative people cannot build the future if they reject the past, for they can develop only if they accept it first and recognize their part in it. In short, people like Dee should put the past to work as a part of their continuing, living consciousness.