Gatsby is caught up in the idea of the "American Dream." This is the concept that anyone, no matter how poor, has the opportunity to achieve prosperity and success if they work hard enough.
Born to poor farmers in North Dakota, Gatsby's childhood is marked by financial struggle. After meeting the "golden girl" Daisy Buchanan as a young man, he becomes obsessed with the idea of accumulating wealth, to prove himself worthy of her.
Motivated by a feeling of shame about his past and a desire to impress Daisy, Gatsby sets his sights high and eventually achieves a spectacular level of wealth through organized crime. When Gatsby is introduced at the beginning of the novel, he has everything we might associate with extreme affluence: a sprawling mansion, millions of dollars, and a top-of-the-range sports car to boot.
Despite all this, Gatsby still yearns for something else: his dream is much deeper than the materialistic accumulation of wealth. This is symbolized by the image of Gatsby reaching for the green light on Daisy's dock. On the one hand, he yearns for the acceptance of the affluent in East Egg, and on the other hand, he yearns for Daisy Buchanan.
Gatsby soon realizes that despite his financial success, he is still not respected and accepted by the upper-class social circles of East Egg. The likes of Tom Buchanan and Daisy were born into wealth, which is something Gatsby could never relate to. No matter what Gatsby does, or how much wealth he accumulates, he will never be respected and regarded in the same way as someone who has enjoyed affluence and privilege from birth.
Gatsby symbolically lives in West Egg, while East Egg (the home of old-money affluence) is an elusive, inaccessible place, always out of Gatsby's reach. As Gatsby reaches for the green light, he is also reaching for the social acceptance he will never be afforded. Appropriately, the light is green: the color of money.
As the green light sits at end of Daisy's dock, Gatsby's yearning also represents his desire for Daisy's admiration and affection, which is a crucial part of his dream. For Gatsby, Daisy represents a doorway into the upper-class community he has been excluded from.
Gatsby's dream has everything to do with social acceptance: he wants to be seen and respected by those in the upper-class circles and to distance himself from his impoverished upbringing. Although Gatsby has achieved the American Dream on all accounts, he still longs for something else. This represents the failure of money and wealth to give him what he truly longed for: love and acceptance, and respect.