Dancing is a central metaphor in Pride and Prejudice, as Azar Nafisi points out in her book Reading Lolita in Tehran. In particular, Nafasi teases out the particulars of eighteenth-century (and early nineteenth-century) dance as a social, communal form:
Forward, backwards, pause, turn, turn, you have to harmonize your steps with the rest in set, that's the whole point.
Dance in Pride and Prejudice involves the same back and forth as courtship: you move toward your partner and away, hold hands, then back off, then come back again. This is a metaphor for the relationship of Darcy and Elizabeth, as well as Jane and Bingley, each couple coming closer, then moving apart, then coming together again. And all of this dancing and courtship is performed--Nafisi emphasizes the aspect of performance-- in the context of a larger society. This is no private waltz, but dancing in a line with other people, and Darcy and Elizabeth or Jane and Bingley must necessarily be conscious not only of each other, but of the society around them.
Mr. Collins ineptness in dancing, constantly trodding on Elizabeth's toes, becomes a metaphor for his ineptness as a lover, a contrast to Elizabeth and Darcy's deft dance steps. Charlotte does not have any desire to prolong the dance (or courtship) with him and marries him quickly.
Piano playing acts as a metaphor for self-discipline and self-awareness. Lady Catherine de Bourgh's contention that she would have been a good piano player had she ever been taught represents her lack of self-awareness, and represents her fantasies about her power that will culminate in her futile attempt to forbid Elizabeth from marrying Darcy. Elizabeth, on the other hand, actually knows how to play the piano--and knows her own limitations, which becomes a metaphor for self-awareness and taking responsibility for one's flaws. When Darcy says he lacks social skills as if this is an excuse, Elizabeth says to him:
My fingers ... do more over this instrument in the masterly manner which I see so many women's do ... I have always supposed it to be my own fault--because I will not take the trouble of practising.
Elizabeth's "fine eyes," a repeated focus of Darcy's admiration, become a metaphor for the mixture of beauty, intelligence and liveliness that attracts Darcy to her.
Finally, homes function as metaphors. Charlotte's home with Mr. Collins, with its careful arrangement of rooms, gardens and poultry to keep the couple separated as much as possible becomes a metaphor for Charlotte's skill at arranging her life. Likewise, Pemberley's order, natural beauty and grandeur become a metaphor of Darcy's virtues:
Elizabeth saw, with admiration for his taste, that it [the furniture] was neither gaudy nor uselessly fine; with less of splendour and more real elegance ...
In short, Austen uses the setting of a gentry women's life: dances, houses, and piano-playing, as metaphors for courtship and character.