Explain irony in the title of the novel Great Expectations.

One type of irony is when event turns out the opposite of what one expects.
Pip learns he has "great expectations" when an anonymous benefactor provides the money so that he can be established as a gentleman. Pip believes his benefactor is Miss Havisham. He thinks she wants to elevate him so that he can marry her ward, Estella, who represents a refined, high-status life to him.
Ironically, Pip learns instead that his great expectations come from the convict, Magwitch, a man he helps as a child. Magwitch has become wealthy in Australia and wants to repay Pip. Pip is horrified that he owes his wealth to a convict and no longer sees it as a great expectation. He also discovers that Miss Havisham raised Estella to be cold and break Pip's heart, just as Miss Havisham's own heart was broken. She never wanted Estella to marry Pip. Finally, Pip learns that Estella, who is a symbol of refinement to him, is the convict Magwitch's daughter. All his great expectations have turned out to be the opposite of what he thought they would be.
Ironically, Pip learns that his great expectations lie not in wealth or climbing the class ladder but in personal growth, generosity of spirit, and learning to value the simple things in life. As he learns to appreciate people like Magwitch and Joe, he becomes a better person and begins to build his life on a solid foundation.