The quote "Cinderella never asked for a prince. She asked for a night off and a dress", comes from Young Adult novelist Keira Cass, author of the 'Selection' series of best-selling novels. To my mind, the quote deals with stereotypical female aspirations.
In the popular fairy tale and Disney film, Cinderella asks her Fairy Godmother to help her attend the glamorous ball to be held that night. To do this, Cinderella needs time away from performing the chores requested of her by her Ugly Sisters, and a dress fit for such an occasion, as she is dressed only in rags.
Kiera Cass' point is that Cinderella doesn't ask for a man to rescue her, by falling in love with her and asking for her hand in marriage. Between the two women, Cinderella and the Fairy Godmother are able to deal with the problem of the dress and attending the ball, just as Cinderella intended. The girls can do it for themselves!
Keira Cass made the comment during an interview with a journalist working on behalf of the San Diego Comic Convention, during which she also observed that being married to a prince is as much hard work as serving the Ugly Sisters, and Cinderella may not have wanted to become royalty, but had no choice if she wanted to marry the prince. This way, it's also a quote about lack of choice for girls in life, as well as their personal ambitions.
Kiera Cass has her own YouTube channel and often discusses her work, as you can see here: