The green light that Gatsby looks out at from his backyard is located on Daisy’s dock. This light represents two different things to Gatsby. First and most obviously, it symbolizes Daisy – when he looks at that light he is thinking of Daisy. The second thing that this green light might represent to Gatsby is his envy (since green is the color of envy) or jealousy toward Tom for what he has that Gatsby wants – Daisy. Nick also makes mention of this green light at the end of the novel, saying that it is what everyone reaches for; therefore, it is also possible that this green light is also a symbol of the American Dream for Gatsby.

It symbolizes the attainment of his goal:  Daisy.  He first sees the green light at the end of the dock at her home.  As his character becomes more clear to Daisy and she comes to the conclusion that his wealth has not come from honest dealings, the green light becomes enfolded in fog and mist.  It signifies at this point in the book that he will not achieve his goal of Daisy as his wife and mother of his children.

Fitzgerald, a master of symbols, makes the color green significant in his novel:

"The green, introduced first as the light at the end of a dock, has ambivalent interpretations. Green typically is associated with growth, spring, and new life. It signals “Go! Go! Go!” presumably for any generation. It is the color of money. All of these meanings apply in The Great Gatsby. Primarily, it is connected with Daisy, who turns out to be an unworthy dream. Colors, then, not only vivify images and create a picturesque vista for the reader but also facilitate Fitzgerald’s thematic commentary about reality and dreams."

(http://www.enotes.com/great-gatsby/chapter-1-summary-analysis)

The green light in particular is a sight that makes Gatsby "tremble." For him it is a beacon, a north star that points to his great love, Daisy. In chapter one, it is Nick who sees Gatsby look watch this light and stretch out his arms to it--a gesture full of longing and desire.

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