Social class is crucial to the plot of this novel because it is in pursuit of his so-called "great expectations" that Pip learns that money does not buy happiness. There are 3 classes of people in the novel, set in Victorian England - poor, middle class and very wealthy. Only the poor people are happy - Joe and Biddy, the Pockets, even Magwitch. The middle class are hypocrites who are always trying to lord it over the poor and suck up to the rich (Uncle Pumblechook), and the rich are miserable (Estella, Miss Havisham).
This novel, like many of Dickens' works, shows that inherited wealth or class status does not help a person become a decent human being. Mrs. Pocket, for example, is a totally worthless wife and mother because she thinks she has been born into an aristocratic family and spends more time reading books about titles than caring for her family. Magwitch has acquired wealth, but not inherited it, and although he is a convict, he has a good heart and is happy when he sees how he has helped Pip.
Read about it here on eNotes on the themes section.
With the creation of a new working class as a result of the Industrial Revolution, there was also the creation of banking houses as new money caused new needs. Heretofore, The Bank of England, which had been established in 1694, exchanged money with only a few well-known gentry as well as dealing with the English government. But, with the rising middle class, there was much more exchange of money as new businesses needed to borrow money and as the rapid production of goods brought wealth to both lenders and borrowers. Those with enough money began to build up the towns outside London; Wemmick's house is such an example.
Because money was more in exchange and it provided opportunities for a better living, the rising middle class began to greatly value it as a way to better themselves. Thus, many perceived the very wealthy as superior to them and, thus, as those they wished to emulate. However, Charles Dickens's perspective of the wealty was that they were a frivolous aristocracy often without the true values that the poor possessed.
In order to illustrate this motif of the frivolity of the aristocracy and the covetous middle class, Dickens created the eccentric character of Miss Havisham and the "base swindler" Uncle Pumblechook and the envious Mrs. Joe. As Pip observes their awe of the eccentric Miss Havisham, he concludes that he will be happier and a better person if he becomes a gentleman. For, after his visit to Satis House, Pip is ashamed of his home with the uneducated Joe, his coarse boots, his being "common" [meaning low-class] and apparently inferior to the beautiful Estella.
This influence of the idea of the superiority of social position is what drives Pip to become less of a person, not more. He becomes snobbish and avoids visiting Joe, he speaks in a condescending manner to Biddy, he servilely seeks the love of Estella, and he is repulsed by the appearance of Provis and the knowledge that the old convict has been his benefactor rather than the upper class Miss Havisham. After his "baptism" by Mrs. Joe at the pump to clean him for his first visit in Stage I, Pip is "purged" of his selfishness and snobbery in the fire at Miss Havisham's in Stage III so that he returns to the true values which Joe has instilled in him. It is then that Pip learns that social class is not the measure of a person's worthiness.