So, this is one those chapters that doesn't advance the plot or anything, but instead gives us some more details and biography about the characters.
First up, Lady Crawley. Sir Pitt's first wife had been a very high-class, aristocratic lady. They did not get along too well. So the second time around, he decided to marry down, picking the daughter of an ironmonger (we'd probably call him a hardware store owner).
The narrator has a sarcastic little tidbit telling us that if Lady Crawley had been allowed to stay in her own socioeconomic class, she would have been a pretty happy, if somewhat silly, wife. As it is, she no longer has any friends. Her old friends are too low-class for a Lady, but her low birth makes her too low-class for other aristocrats. She is kind of dumb, and since she no longer has her good looks, she exists as "a mere machine in her husband's house, of no more use than the late Lady Crawley's grand piano." She doesn't even have "character enough to take to drinking." (9.4) Ouch.
OK, enough about her.
Now for Mr. Pitt Crawley, Sir Pitt's oldest son. He's prissy and a little compulsive with the whole acting-like-a-gentleman thing. He's so fixated on manners that at college his nickname was "Miss Crawley." Kids can be so cruel.
Mr. Crawley is also very ambitious, and the narrator mocks him for having "a mediocrity which ought to have insured any man a success" (9.9). Get it? The joke is that only the average and boring get promoted.
So far, Mr. Crawley's ambitions haven't gotten too many results. He's published some articles and is active in the government of the county. These achievements are meant to sound way lame.
So that's Mr. Crawley.
Here's a bit more about Sir Pitt: his cheapness and general bad nature make him a poor money manager. In the long run, he doesn't invest in his estate – which decreases any money he could make from it. And he is a horrible landlord and people person – which means that no good people will work for him and he is constantly swindled by the thieves that surround him.
Now, more about the family finances.
Sir Pitt still owes Mr. Crawley a bunch of money. This is money that Sir Pitt's first wife left to her eldest son (Mr. Crawley), but which Sir Pitt has yet to give to Mr. Crawley. Probably because it's already been spent.
And finally, one more family member. Sir Pitt and his brother Bute have a half-sister, Miss Crawley. She is super-rich and has no children. Both Sir Pitt and Bute really, really want her money. And even maybe more than that, they want the other one not to get any of it.