What is Gatsby's dream?
Very often, Gatsby's dream is likened to the broader concept of the American Dream. In economic terms, the American Dream refers to the conditions of capitalism, conditions which are supposed to allow upward financial mobility for any and all citizens. Gatsby embodies this aspect of the American Dream due to his humble origins. Through initially shrouded by gossip and intrigue, it is eventually revealed that Gatsby was actually born into a poor farming family, and his subsequent accumulation of wealth can be interpreted to exemplify the possibilities inherent in a mixed/free-market system. Likewise, Gatsby's dream of "acquiring" Daisy could be interpreted as an extension of the American Dream in that Daisy is, in some ways, presented as a commodity that Gatsby wishes to consume. This depersonalized interpretation takes into account Gatsby's extensive efforts to accumulate wealth in order to be considered worthy of Daisy's affection, and indeed, Gatsby admits to Nick Carraway that his (Gatsby's) lavish mansion was purchased as a means to be close to Daisy and to prove to her the extent of his affection. Therefore, Gatsby's dream of winning Daisy's love is indelibly linked to his economic pursuits, and his rise from humble origins to incredible wealth showcases how much Gatsby's dream and the American Dream are intertwined, at least in economic terms.
Gatsby's dream is nothing less than turning back time. He left his beloved, Daisy, to go fight in World War I. In the interim, she married Tom Buchanan. Gatsby returned, made his fortune and bought his mansion across the bay from her in order to woo her back, for to him Daisy represents the wealth and financial security he has always craved, as well as his youth. He believes he can convince her to leave Tom and marry him. He dreams of erasing the time since she married Tom, so that they can start over as if Daisy's marriage had never happened. Nick tries to tell him this is impossible, but Gatsby dismisses Nick. Gatsby shows a bit of shock over Tom and Daisy's young daughter, Pammy, who is impossible to erase, but he seems determined to overlook that. Nick proves right that it is impossible to erase time, as Gatsby learns when Daisy shows she is unwilling to deny a recent past that is real and potent for her. As Tom says, he and Daisy have shared things that nobody else can understand. Daisy says she can't do what Gatsby wants and say that she never loved Tom.
Nick ties Gatsby's dream of starting over to the American dream of Europeans as they stood on the cusp of the New World, dreaming of starting afresh, creating a new world as if the past had never happened.
Gatsby's dream is to be good enough for Daisy. However, this is never fully possible simply because of the fact that Gatsby was not born into a wealthy or prestigious family. Even as a boy Gatsby was constantly focused on improving upon himself. This is evident in this quote about Gatsby's "General Resolves" as a child:
No wasting time at Shafters or [a name, indecipherable]
No more smoking or chewing
Bath every other day
Read one improving book or magazine per week
Save $5.00 [crossed out] $3.00 per week
Be better to parents (9.104)
Gatsby has been ambitious from a young age, but his discovery of Daisy redirects this energy into an almost obsessive goal of five years. Gatsby is in constant denial that he will never be equal to people and like Tom and Daisy in the eyes of society because of his background. When Nick tells Gatsby "You can't repeat the past," Gatsby replies with "Can't repeat the past? Why of course you can!" Gatsby believes that he can erase the parts of his past that make it harder to get to Daisy and repeat the times when he almost had Daisy. What he doesn't understand is that for a woman like Daisy, Tom Buchanan is a secure object and has been since the day he was born, because he comes from a rich Chicago family. This is why Daisy won't tell Tom that she never loved him, and leave him for Gatsby.
Gatsby believes heavily in the American Dream, the belief that he has as much a right to a woman like Daisy as someone like Tom. However F. Scott Fitzgerald makes it clear that that the American Dream is not fully possible. Gatsby may be an extremely wealthy man, but Tom will never respect him as an equal. Gatsby's inability to reach Daisy and the way he literally dies trying symbolizes classism in America. In conclusion, Gatsby's dream is to be equal and good enough for Daisy, and equal or better than Tom so that Daisy will be able to confidently leave her husband for him.