Fitzgerald submitted several titles to his publisher (among them Under The Red White and Blue and Trimalchio in West Egg) before settling on the simple and alliterative The Great Gatsby.
The title of the book is very much like Nick's presentation of the man: it is initially built up, then dismantled, and then built up again. In other words, Gatsby is first "great" to Nick, then not so "great," and then "great" again by the end after his death.
So, what made Gatsby "great" to Nick? His dreams. Whereas Nick has no clear desires in the novel, Gatsby has only one: Daisy. Nick idolizes Gatsby's megalomania, his romanticism, and his ability to reinvent himself. In other words, Gatsby is the embodiment of "The American Dream," which says that anyone (especially a poor farmer boy like James Gatz) can go from "rags to riches" and move up the social class ladder (from the Midwest to West Egg) almost overnight. Nick wishes these dreams for himself and all Midwesterners too.
But, Nick also realizes that there is "great" risk in a single-minded dream centered around wealth and women. Gatsby's "greatness," like his name, party guests, and library books is all a facade. It was a myth invented to give the illusion of greatness. Really, Gatsby is an opportunist who used Prohibition and his connections (Dan Cody and Meyer Wolfsheim) to amass wealth by illegitimate means (bootlegging, gambling, racketeering). In the end, Gatsby is murdered, with no friends, family, or lasting legacy (no one, except his father and Nick, attend his funeral).
Gatsby's greatness parallels his dreams. As it pertains to the American dream, Gatsby is great: he achieved all that he set out to. But, in a closer examination, he used underhanded means to achieve greatness. So, the title is a kind of paradox which shows the levels of contradictions (between wealth and success) in Gatsby, Nick, and America.