Pip, an orphan and adopted son of his much older sister and her husband, Joe, who is a blacksmith, has every reason to expect to live a humble, ordinary life as the novel opens. He himself may expect to become a blacksmith like Joe.
In this way, he is like the majority of young people in the United States today. He doesn't have $250,000 in the bank to pay for college, and he doesn't get large monthly checks from a trust fund. He has to expect to scramble into whatever life he can find.
But suddenly that all changes. An anonymous, wealthy benefactor is going to bankroll him. Suddenly, he has the chance to get the Victorian equivalent of a top-notch education, and a big monthly check is put in his pocket. Now he has "great expectations": with the benefactor and the money, Pip can expect to go far in life, to be important, not just an obscure laborer.
Pip assumes his benefactor is Miss Havisham, whom he thinks is grooming him to marry Estella. He couldn't be more wrong. His benefactor is the convict Magwitch, whom Pip helped at the beginning of the novel. He couldn't more horrified—but as part of his maturation, learns to come to terms with it and value Magwitch's good heart.