As you probably already know at this point, Miss Havisham is a character from Charles Dickens's novel Great Expectations. For more background on her role in the novel, check out "In a Nutshell."
The Miss Havisham we see in Duffy's poem is slightly different from the one in the novel. The character in the novel seems bitter and unhappy, that's for sure; but there's an angriness and passion in this poem that we don't see in the novel. In Duffy's poem, Miss Havisham puts it all out there – her pain, her longing, even her erotic fantasies (and those definitely do not exist in the book!). Duffy brings out an imagined, hidden side of Miss Havisham. It's not pretty, but it adds depth to her character, and it stokes our pity for her even more than in the novel.