The character Meyer Wolfshiem in The Great Gatsby allows Fitzgerald to satirize the American Dream and the Roaring Twenties. Wolfshiem is also used to reveal details of Gatsby's business.
Wolfshiem is a Jewish gangster (some think this reveals anti-semitism on Fitzgerald's part) who fixed the 1919 World Series (in the world of the novel). He also, presumably, is a bootlegger. He lives "under the radar," as they say, trying to not draw attention to himself so that the police do not pay too much attention to him. This, suggests the novel, is how one gets rich in America and fulfills the American Dream.
Wolfshiem as a character also helps the author reveal the shallow nature of the people in the American twenties. He claims to be such a good friend to Gatsby, yet he won't even attend his funeral. He is self-centered and superficial and hypocritical.
Wolfshiem, together with people like Daisy and Tom and Jordan, is what the American Dream is all about in The Great Gatsby.
Gatsby's connection with Wolfshiem also reveals a bit about Gatsby's business. While Gatsby's occupation still remains somewhat of a mystery, the romance is certainly taken out of the issue. His work puts him in the league with Wolfshiem, and that's not a good league.