In the novel, Gatsby is defined by his dreams, and his life is determined by them. It could be said that he, in fact, died for the greatest of his dreams--to repeat his past with Daisy. It is important, however, to recognize that there is a significant difference between Jimmy Gatz growing up in North Dakota and Jay Gatsby of West Egg.
As a boy, Jimmy Gatz dreamed of a successful life far removed from his poverty-stricken upbringing. He longed for romance and beauty, a glamorous life infused with mystery and enchantment. He hoped and dreamed, but he also worked and planned. His journal shows his attitude and efforts to secure the future he wanted. After running away from home, he attended college for a short time, but soon left. He did not want to continue working as a janitor to pay his tuition, and he was in a hurry. He had no time or inclination for work and study, as he once had. Even though his attitude had changed at this point, his dreams were still possible--until he meets Daisy.
After he meets the beautiful and wealthy Daisy Fay in Louisville, she becomes the embodiment of all his early dreams; his romance with her one summer determines the rest of his life. Throwing in with a gangster (Wolfsheim), Gatsby soon amasses a fortune. With money, he believes, he will belong in Daisy's privileged world and can win her back. His dreams are not fulfilled, however, and his story ends in tragedy.
One especially important lesson can be drawn from Gatsby and his dreams. As a boy he seemed to be on the right path in pursuing them, but when Daisy became his great dream, he was doomed to failure. The reason? This dream of Daisy was rooted in an illusion instead of reality. He did not recognize the reality of his relationship with Daisy. By the circumstances of his birth, he was excluded from privileged social class; no matter how great his wealth, he would never belong in Daisy's world. He would forever be an outsider, making his dream an impossibility. Furthermore, as Nick tried to make him understand, nobody can ever repeat the past.
The essential lesson here seems to be this: In order to achieve our dreams, they must be realistic and lie within the realm of possibility. Dreams based on illusion become illusions themselves.
In many respects, The Great Gatsby presents a picture of the failed American dream in the case of Gatsby himself. He fell in love with a girl who was above him in certain respects and by all accounts she fell for him as well. But upon returning from the war, he was beneath her and so he fought and worked and made himself into a wealthy and powerful individual. Yet it still wasn't enough, he failed to completely re-invent himself, suggesting that perhaps in the end it is impossible to realize that aspect of the American Dream.
Gatsby's hope is never destroyed, even when everything is crashing down around him, he still appears to have hope that things will work out, that Daisy will return to him.