We know that he has a reputation and that he is at least a bit dramatic. He is mentioned in conversation, but only briefly. Then he is depicted as standing on his balcony in the night and reaching out his arms as if to reach across the water.
Not much on a personal level. We know, according to Carraway, that "there is something gorgeous about him," that he lives in West Egg (the less fashionable of the two "Eggs" in the novel) next door to Nick Carraway, and that his name makes Daisy jump for some reason. He is described as having "leisurely movements" and "secure" footing as he walks across his lawn. In short, he is a mysterious man and we readers certainly have our interest piqued after having read Chapter 1.