Mrs. Gardiner replies to Elizabeth's letter and lets her know that Mr. Darcy left his house a day after Elizabeth had. He went to London and located Mr. Wickham and Lydia.
Darcy tried to induce Lydia to leave Mr. Wickham, but she wouldn't, assuming they would marry at some time or another.
Wickham was definitely not keen on the idea of marrying Lydia, since he still hoped to make his fortune through marriage.
Darcy settled Wickham's debts and gave him the fortune he desired so as to marry Lydia.
This was all to be kept secret, however, Mrs. Gardiner cautions Elizabeth. She writes that she likes Mr. Darcy very much and he was very sly, never mentioning Elizabeth at all. She hopes Elizabeth will not be angry with her for bringing the subject up.
Elizabeth doesn't know whether to feel pain or pleasure, but she knows how obligated she is to Mr. Darcy for his utter goodness. Mr. Darcy had met with a man whom he despised and bribed him to do the right thing for a girl for whom Mr. Darcy could have little respect.
Elizabeth wants to think he did it for her, but can't possibly believe that it's true, given her behavior towards him after his proposal.
She goes out walking and Wickham joins her. He fishes around to find out what she knows about his past. Elizabeth admits to him what she knows, but in a genteel manner, and she lets him know that she wants bygones to be bygones. They are brother and sister now.