The term "great" as used in the title of The Great Gatsby is part hyperbole, part ironical, and part true, as Nick relates Gatsby's story to the reader.
The story occurs in the roaring twenties, when pomp ruled and money was flowing in and parties like those thrown by Gatsby were popular. Exaggeration was common place, and this probably contributes to the title.
But calling Gatsby great is also partly ironical. Does fulfilling the so-called American dream the way Gatsby does make one great? He is a poster boy for the American dream, but look how he achieves it.
Finally, Gatsby loves like every human should love. His love is all-encompassing and relentless. Gatsby is a great romantic. In this sense, he fulfills expectations of being called great. Whatever else The Great Gatsby is, it is first a love story.
I think Gatsby is referred to as the "Great" because he has qualities like a magician. Many magicians take a stage name that starts "the great ____________"
He is able to make things disappear (his profession, Daisy's crime, the woman's messed up dress). He is also able to make things reappear (a relationship with Daisy)
He also works with great effort toward every goal. He doesn't do anything half-heartedly. A good magician will make it happen, Gatsby does this throughout the book, but unfortunately to 3 peoples deadly detriment.
To the extent that Gatsby is great, it is because he represents something that is great to Nick. Specifically, Gatsby represents a pure desire to improve himself and to get ahead in life. This is something that both Nick Carraway and the author identify with the Midwest, the "good" part of the country.
Unlike the other people in the book, Gatsby is not a phony. He is doing what he does because he is pursuing a dream. Because he pursues the dream intensely, with his whole heart and soul, he is admirable in Nick's eyes.