Jay Gatsby is Fitzgerald's example of the American Dream incarnate. He is a man who, when Nick meets him, appears to have it all: immense wealth and the ability to live a riotous, decadent lifestyle. Yet, as the novel emerges, the reader and Nick come to understand how Gatsby had to battle to create this wealth and the kind of figure that he presents. He was a young man who from his youth rejected his humble origins and did everything he could to raise himself up in the world. His impetus and motivation for gaining wealth was his love and desire for Daisy Buchanan, who he met before going to fight in World War I. Gatsby became enamoured of her wealth and charm, and deceived her about his own origins in order to persuade her that he was good enough for him. Even though Daisy promised to wait for him to return, she married Tom Buchanan whilst Gatsby was studying at Oxford in order to educate himself. At that point, Gatsby, with a single-minded determination that Nick is in awe of, focused solely on gaining Daisy, and his acquisition of wealth and property and his parties are all designed to help him achieve this goal.
What distinguishes Gatsby therefore from other characters is his single-minded focus, determination and optimism. He believes so strongly that he is able to do whatever he sets his mind to, and the charisma that such a belief gives him is something that impresses Nick. Note the following quotation that comes in Chapter 3, as Nick meets Gatsby for the first time:
He had one of those rare smiles with a quality of eternal reassurance in it, that you may come across four or five times in life. It faced, or seemed to face, the whole external world for an instant and then concentrated on you with an irresistible prejudice in your favor. It understood you just as far as you wanted to be understood, believed in you as you would like to believe in yourself.
This is what makes Jay Gatsby such a remarkable figure as it captures both the imagination and the hope that Gatsby characterises and that he has used to re-make himself, showing himself to be a perfect example of the American Dream. Gatsby's importance, therefore, lies in the way in which he is used as a representation of the American Dream--both its potential and its ultimate failure.