Elizabeth realizes that her parents don't exactly have a model marriage (you think?), and she feels bad that her father makes fun of his wife all the time.
This is a key moment for Lizzy, because she finally starts to see that her dad is partly to blame for the family, too. He could have intervened with the kids, helping to make sure the daughters grew up into respectable young women by, say, hiring a governess.
Instead, he just spends all his time in his library avoiding his wife.
Lydia is apparently having a grand time buying gowns and flirting in Brighton, and now it's time for Lizzy's second trip, her summer holiday with the Gardiners.
But there's a change of plans, and they're not going to the Lake Country after all: they're going to Derbyshire, which—dun dun dun—just so happens to be the location of Mr. Darcy's estate Pemberley.
Of course, Mrs. Gardiner wants to visit Pemberley.
Historical Context Lesson: Proper middle-class folk, like Elizabeth and her family, could visit grand estates belonging to people like Mr. Darcy. Think of it as their version of MTV Cribs, except they get to do it in person.
Elizabeth doesn't want to go, for obvious reasons.
It's cool, though: the chambermaid at their inn lets her know that the family isn't down for the summer, which means there's no risk of running into Darcy.