In The Great Gatsby, what does the green light at the end of the Buchanan's pier's symbolize?
That light symbolizes all of Gatsby's hopes and dreams. On the very second page of the book, Nick says of Gatsby,
...it was an extraordinary gift for hope, a romantic readiness such as I have never found in any other person...(6).
Of course, Gatsby's yearning is for Daisy, who is herself a symbol of all that Gatsby aspires to, the American dream, the idea that everyone can succeed here, no matter how humble the beginnings, by working, wishing, and hoping. Everything that Gatsby has done since he met Daisy has been with the aim of acquiring her. He believes that if he does so, he will have achieved the American dream. Of course, given who Daisy is, that dream, had he achieved it, would have been an empty one, and his dying might be the more merciful end for him, rather than his having lived and learned that his dream was rotten to the core.
Green represents hope and renewal, but in addition, one could surmise that the use of vehicles in the book could also make green represent that things are allowed to commence, continue, or to go.
In essence, as long as there is a green light, Gatsby has permission to move forward and attempt to attain his dream (Daisy). The irony is that Daisy is not the one who has placed this light out there for him. Carroway, as our narrator, describes the light as "minute and far away" (Gatsby 16), implying that even as the book starts, any real chance of Gatsby actually completing the dream are also minute and far away, even though they are in his sight.
When that light goes out late in the novel (the realization at least to Nick), hope is also gone, and in essence foreshadows Gatsby's tragic end.