It is in Chapter 21 that Pip, now a man with expectations, meets Herbert Pocket again. He realises that Herbert was the young boy that he fought in Satis House in Chapter 11. Herbert Pocket is now grown up and though witout prospects and poor, he is clearly a gentleman and beings instructing Pip in the manners of a gentleman in Chapter 22 very sensitively. Jaggers has organised for Pip to stay with Herbert, and it is to be Herbert's father, Matthew Pocket, who will be entrusted with Pip's education to transform him into a gentleman. It is Matthew Pocket who is related to Miss Havisham and this explains Herbet's presence at Satis House in Chapter 11.
Herbert Pocket is a young London gentleman who becomes Pip's roommate and best friend. Mr. Jaggers, Pip's guardian, has arranged for Pip to live with Herbert so that he can acquire the manners and good and bad habits of a gentleman from this well-mannered but impecunious youth. When Pip first meets Herbert in London he realizes that this was the same person he had a fight with at Miss Havisham's house when they were young boys. Herbert had illusions about being a boxer and challenged Pip to a boxing match, which Pip quickly won.
Herbert is the son of Matthew Pocket, who becomes Pip's tutor, also by arrangement with Mr. Jaggers. Both Matthew and his son are related to Miss Havisham. Their connection with her and with Pip's guardian Mr. Jaggers serve to convince Pip that Miss Havisham must be his secret benefactress. Herbert does not know anything about this but assumes that Pip is probably correct in his deductions. Pip goes further in his deductions. He assumes that Miss Havisham is having him taught to be a London gentleman because she intends to have him marry her adopted daughter Estella and to leave them all her money with which to live a life of luxurious indolence.
Since Miss Havisham never married or had any children, she has no close relatives. Matthew Pocket is one of her distant relatives, and Herbert therefore is slightly more distance. Miss Havisham has several other distant relatives who are continually visiting her and expressing their deep affection for the old lady because they hope to inherit some of her money. They all hate Pip because they are afraid he might get exactly what he dreams of when Miss Havisham finally dies--that is, the hand of Estella in marriage and the bulk of the old spinster's fortune. She enjoys tantalizing all these distant whom Pip sees as toadies and humbugs when he first encounters them at Miss Havisham's home in Chapter 11.
Herbert is useful to the plot of Great Expectations because he is instrumental in teaching Pip the manners, tastes, and values of a gentleman. He can also tell Herbert a lot about Miss Havisham's family history, and useful when Abel Magwitch makes his appearance in Chapter 39. Pip discovers that Magwitch's return to England is known to the authorities and that he must get out of the country immediately or face hanging. Herbert helps Pip practice rowing on the Thames and then tries to help him catch a steamer bound for Hamburg or another steamer bound for Rotterdam on the outgoing tide. But they are betrayed by Compeyson, Magwitch's arch-enemy, and Magwitch ends up in the prison hospital ward in grave condition because of his age.
Pip later persuades Miss Havisham to give Herbert enough money in secret to enable him to purchase a partnership in a small East India business enterprise and to marry the girl he loves.