I think that the answer you are looking for is in Chapter 5. It comes just before Nick and Daisy and Gatsby go over to show Daisy around Gatsby's house.
Nick asks Gatsby how he made his money -- what business he was in. Gatsby basically tells Nick that it is none of his business and that he should butt out. Then he realizes that that was a rude thing to say and he backs off and says that he was in a bunch of different businesses.
I think he hardly knew what he was saying, for when I asked him what business he was in he answered, “That’s my affair,” before he realized that it wasn’t the appropriate reply.
“Oh, I’ve been in several things,” he corrected himself.
Gatsby's source of wealth is one of the novel's mysteries, though Tom will uncover him as a bootlegger. Gatsby at first tells Nick he inherited his money. Later, when Gatsby mentions to Nick that "it took me just three years to earn the money" to finance his mansion, Nick questions this, saying he thought Gatsby had inherited his fortune. Gatsby revises his story on the spot, agreeing that he did inherit, but explains that he lost it all in the "panic of the war." When Nick then asks what business he is in, Gatsby's congenial mask slips, and he tells Nick to mind his own business, revealing that this is a touchy topic. He catches himself, however, and says he's been involved in several things, then mentions the drug business and the oil business, but notes he's not in either now.
Gatsby's business dealings are shady, but we do learn later that he inherited $25,000 from Cody, money he never saw.