Gatsby moved in to the house on the West Egg side and from his house he can see very faintly a green light that is at the end of Daisy's Dock on East egg. Gatsby fell in love with Daisy years ago before he went to war. He has not seen her since and he is very obsessed with meeting with her one again.
To him the Green Light means hope and his dreams of once again being with Daisy. Whenever he sees that light he thinks of her and how much he loves her. That green light also means Gatsby's jealousy of Tom, Daisy's husband. Gatsby is jealous because he feels he should be married to Daisy and the phrase "green with envy" backs this statement. He feels that he and Daisy would be very great together and wants Nick to bring them together.
In Chapter One of The Great Gatsby, he reaches from his house toward that green light as if reaching for his ultimate goal, Daisy. The fact that it is very distant and barely visible lets us know that it is a dream that wont come true. The importance of the light is very significant because it gives us something on which to attach the longing Gatsby has for Daisy.