The next evening, we're treated to a conversation between Mr. Darcy and Miss Bingley. Miss Bingley throws a steady stream of compliments and requests at Mr. Darcy, who keeps shutting her down.
Apparently Mr. Darcy is a good judge of character, too.
Mr. Bingley, Mr. Darcy, and Elizabeth discuss the merits of changing your mind because a friend persuades you to. Mr. Darcy says that you're a fool if the only reason you yield to a friend's opinion is because they have that opinion.
In other words, don't act just to please somebody else. Elizabeth, alternatively, argues that a trusted friend's opinion should be enough to sway you.
Not to hit you over the head with it, but this discussion is foreshadowing later parts of the plot, like when Mr. Bingley will be persuaded by Mr. Darcy that Jane doesn't care about him, even though his own heart says otherwise.
Elizabeth notices how frequently Mr. Darcy looks at her, but figures he can't possibly be interested in her. Ergo, he's looking at her to find things to criticize.
The group listens to Mr. Bingley's sisters play the piano and Mr. Darcy asks Elizabeth if she would like to dance. She ignores him and he repeats his request. She responds that she would rather not give him the pleasure of mocking her, so no, she will not dance with him.
Miss Bingley gets jealous, realizing that Mr. Darcy is beginning to get really interested in Elizabeth.
As for Mr. Darcy, he is "bewitched" but thankful that Elizabeth's social status is so beneath him that he can't possibly be tempted into any kind of serious relationship.