The green light represents Gatsby's desire to reunite with Daisy, but more universally, it is a symbol of the dreams we all pursue.
The green light shows Gatsby where the end of the dock at Daisy's house is located. It represents Gatsby's desire for Daisy. As the novel opens, she seems so close to him and yet so far away from him, on the other side of the bay, just out of his grasp. On the night Nick returns from having dinner at the Buchanans, he sees Gatsby, whom he has not yet met, stretching out his arms toward the green light, trembling with longing; but Nick does not understand what that gesture means.
As Nick notes later, when Gatsby reunites with Daisy, the significance of the green light fades. It represented Gatsby's hope for a future in which Daisy would be a central part of his life. Gatsby wanted to do nothing less than erase the last five years of their separation, as if they didn't happen. After they reconnect, he says,
Now it was again a green light on a dock. [Gatsby's] count of enchanted objects had diminished by one.
However, the green light remains a potent symbol until the end:
Gatsby believed in the green light, the orgastic [hopeful, promising] future that year by year recedes before us.
Fitzgerald universalizes the green light at the novel's close, saying that like Gatsby, we all "run faster, stretch out our arms further" in pursuit of our dreams.