The color green symbolizes hope. This green light is across the courtesy bay, which separates East and West egg. This light is located on the dock of Daisy Buchanan, the love of Jay Gatsby's life.
Jay Gatsby stares at this light, across the bay, symbolizing the hope that he will once again meet Daisy, and have the possibility that they will have a future together. In the novel it mentions that Jay Gatsby would stretch out his arms to the light, and this would be the closest that he was able to get to Daisy at the time, and is in hopes that this green light will guide him to his goal to be with Daisy once again in the future. Later on in the novel, a heavy mist is in the air, and it covers up the green light, possibly showing that there really isn't hope for Gatsby to get Daisy, and that this green light on the end of Daisy's doc is just a green light and nothing
There is also another meaning for this green light, that doesn't exactly relate to Jay Gatsby's hope to reunite with daisy one day. "in the final chapter of this novel, Fitzgerald compares Gatsby's green light to the "green breast of the new world", comparing Gatsby's dream of rediscovering Daisy to the explorer's discovery of America and the promise of a new continent. It also compares how Gatsby is all into his material possessions, to how America is become fixated in greed and wealth, and all these dreams dies due to the greed and superficiality.
Sources: The Great Gatsby