The title has a double meaning, because when it refers to “great expectations” it is talking about both Pip’s money and his plans for himself; neither worked out for him.
In many ways, Dickens is satirizing the role of money in determining one’s fate. Pip had one life in store for him before the money, and a different one after. Most people would agree that although a blacksmith’s life is not luxurious, having a trade you can be successful in and people who love you is preferable to being isolated in the city with people who pretend to be your friend only as long as you have money.
When Jaggers tells Joe and Pip that Pip has expectations, they gasp. They seem to understand exactly what he is saying.
“Now, I return to this young fellow. And the communication I have got to make is, that he has Great Expectations.” (ch 18)
He also comments that the expectations come with the money to support them. Pip is to be a gentleman. He will be set for life. Everything will be fine from now on.
Ironically, things don't go well for Pip. His life as a gentleman is lonely and full of conflict. He struggles, because he is not given guidance on what to do with the money. The other gentlemen that he associates with seem to mostly waste thiers.
When Pip learns that the money came from the convict, the whole illusion comes crashing down on him. He realizes that he is the same person he was, and he can go back to being that person. He had turned his back on those he loved, but seeing Magwitch sacrifice himself out of a paternal desire to see Pip was enough to return Pip to his simple lifestyle, and become much happier making his fortune, modest though it may be, on his own.
I would say that the title Great Expectations does not apply merely to Pip but to human expectations in general. Pip is deeply disappointed in love, but this is a pretty common experience for men and women in general. He was disappointed in his ambition to become a gentleman, which was an ambition largely inspired by his love for Estella; but this too is a common enough experience for people who manage to climb a few rungs up the social ladder. They often find that the people who were above them are not as good as the people they left below. Life itself is a disappointment for many of us. We expect too much of it when we are young. True love is hard to find. True friendship is equally hard to find. And they seldom last. Troubles are very easy to find, or they find us. The hero of F. Scott Fitzgerald's novel The Great Gatsby is very much like Pip. Gatsby wanted to become a gentleman in order to win Daisy, just as Pip wanted to become a gentleman in order to win Estella. Both are cruelly disillusioned. Gatsby spends a fortune entertaining people and not one of them comes to his funeral--not even Daisy. The words "Great Expectations" are like the first part of an unfinished sentence which might read something like: Great expectations are a bad mistake because they lead to disillusionment and unhappiness. Pip's story is just an example of a general principle.
Expectations of this world
And the people in it,
Are surely the sources
Of our greatest misery.
The Uddhava Gita