Apologies

Late in life, Miss Havisham realizes that her broken heart has been the root of Pip’s similar fate. By raising Estella to spurn men, she may have gotten a twisted “revenge” for being left at the altar, but it has actually negatively impacted real people. As a person who knows the torment of heartbreak, Miss Havisham understands the pain she has caused Pip and begs his forgiveness. With this forgiveness, Dickens makes one of the main morals or themes of the story clear: admission of one’s sin, sympathy for those wronged, and a change of behavior are sufficient atonement for any wrong.

EDIT: Miss Havisham admits to Pip that she has been overly harsh, saying that she wants "to show [him] that [she is] not all stone. But perhaps [he] can never believe, now, that there is anything human in [her] heart." (385). This is an apology, proving that she does want to right the injustices she has caused.