We don't know a lot about Meyer Wolfsheim – and we're not supposed to. Beyond the fact that he's a business associate and a friend of Gatsby's, all we know is that he's an inhabitant of New York's seedy underworld and a dead ringer for real-life Arnold Rothstein: the man who really did fix the 1919 World Series—one of Meyer Wolfsheim's impressive accomplishments (4.118-118).
Although Wolfsheim remains a mystery, we end up learning quite a lot about other characters through him. First of all, his business "goneggtions" with Gatsby shine a rather dubious light upon the latter's dealings. Even though Gatsby wants everyone to believe that he's the real deal, we begin to wonder how he really earned that fortune.
Wolfsheim also reveals some rather unfortunate things about one of our other main characters, Nick, like that he's innately judgmental. Nick is clearly intrigued by the guy, but he also acts like he's got a bad taste in his mouth around him. This shows us the bias against the foreign "Other" (Wolfsheim is Jewish) prevalent in so-called "respectable" society of the time—the same kind of bias that makes Tom declare that the "Nordic race" is being submerged, and the same kind of bias that led just two decades later to the Holocaust.