Gatsby's most obvious dream is to recapture the heart of Daisy after he lost her so many years ago. He also dreams about turning back time, recapturing the past, and going back to their dreamlike courtship when they were younger. For a while, Gatsby seems to come within reach of this dream.
In a larger sense, however, the novel is about the emptiness of the American Dream that says wealth and success are within anyone's reach, regardless of their social status at birth. Gatsby is a man of self-made wealth, but his achievement does not allow him to reach Daisy. She stays with her husband, who comes from an established family of enormous wealth.