Gatsby's ability to hope and to believe in the reality of his own dreams is what makes him gorgeous in a certain way, according to Nick.
This idea is presented in the first pages of the novel as Nick introduces Gatsby as a complex figure, both reprehensible and noble.
"If personality is an unbroken series of successful gestures, then there was something gorgeous about him, some heightened sensitivity to the promises of life.… [Gatsby had] an extraordinary gift for hope, a romantic readiness such as I have never found in any other person and which it is not likely I shall ever find again."
Though Gatsby represents the crass materialism and shallow morality that Nick despises, Gatsby also possesses a special talent for hope. There is an innocence, ultimately, in Gatsby's ambitions and even a nobility that bring Nick to admire the man despite his flaws.
We can characterize Gatsby's aims rather simply. He wants to be great and believes that he can. He feels that he spoiled Daisy's womanly innocence and so wants to do the noble thing and marry her (even though she is already married and has a child).
Before telling Gatsby's sometimes tawdry story, Nick makes sure that he lets us know that Gatsby is not all bad. He is not a villain. Rather, his failures are the failures of a sometimes too-innocent dreamer.
This quote is important because it not only establishes the essence of the Gatsby character but it also foreshadows the very nature of the story and its primary themes: idealism, aspiration, and loss.