As such an eccentric character, Miss Havisham serves easily as a measure for many of Pip's lessons.
1. For instance, her wealth and social class, which arbitrarily give her a status above others, illuminates the ridiculous sycophancy and hypocrisy of Uncle Pumblechook and others such as Mrs. Pocket who aspire to what Dickens considered a frivolous aristocracy. Her very name--Havisham--suggests the spuriousness of her life that is wasted on her desire for revenge against all members of the male sex.
2. And, as the years pass, Pip realizes the terrible toll that living solely for revenge takes upon a person. For, he perceives loneliness that haunts Miss Havisham as her protege, Estella, whom she has brought up to be brutally cold and heartless, is equally incapable of returning the love Miss Havisham gives her. In addition, Pip realizes what a worm vengeance is, eating away at the soul of the one who harbors it. When she finally becomes aware of the terrible hurt she has caused Pip, Miss Havisham begs forgiveness because she does not wish to die with the burden of her guilt.
3. Further, Pip has reinforced by Miss Havisham the lesson that wealth does not buy happiness or ensure success and friends. This is a lesson that Pip apprehends from others as well, but, certainly Miss Havisham presents a living example of the decay that can come to a person who possesses only money and none of the spiritual rewards of life such as friends and loved ones.
4. Above all, Miss Havisham of Great Expectations is a character who serves to develop the important theme of Charles Dickens that Mr. Jaggers overtly states: "Take nothing on appearances." Since the visit of Jaggers to the forge to announce Pip's "great expectations," Pip has believed that Miss Havisham has been his benefactor; however, she has not, just as she has not been anything that she has sought to be. Miss Havisham's life has, tragically, been truly a sham. From her, Pip learns that appearances are often superficial. The true values are in friendship, and integrity. Pip returns to Joe, his loving friend and he learns that he must create his own life and not depend upon the generosity of any benefactor.
Miss Havisham teaches Pip a number of principles.
First, at her house when he comes to visit, she teaches him that he is less than them in terms of class structure. I believe this builds his desire to become greater and it builds his expectations in life.
She teaches him to play the card game, "Beggar my Neighbor." This is the card game he and Estella played as children. This also led him to discover that jacks are called jacks not knaves.
Just before she is badly burned and dies, she teaches Pip that the way she has lived her attitude about men (which she therefore perpetuated in Estella) was wrong. Pip had value and she finally encouraged him to go after Estella, to "love her!"