To me, aside from the fact that Wolfsheim is modeled after the man who supposedly fixed the world series and allows us a glimpse into the underground world of bootleggers and the like to which Gatsby belongs and from which he has gained his fortune, the main thing that he adds to the story was his unique view on friendship. Wolfsheim, in telling the story of his friend who had been shot dead at a restaurant (not an uncommon fate for those who were a part of that lifestyle) remarks that it is best to show your love for a person while he is alive instead of waiting until he is dead. This is a direct parallel to the relationship between Nick and Gatsby. Once we are gone, who we were in life ceases to matter to anyone who was not a true friend. Those who came to the parties moved on to new parties. Gatsby himself was unimportant to them for anything more than what he provided.
In my opinion, the importance of Meyer Wolfsheim up to this point in the book is mainly to show us something important about Gatsby. What Wolfsheim shows us is that Gatsby is really not the respectable businessman that he seems to be.
When Nick meets Wolfsheim, it quickly becomes apparent that Wolfsheim is a gangster. For example, he really likes the place across the street, even though he has a memory of an associate of his getting killed there by (it is implied) rival gang members. Gatsby later tells Nick that Wolfsheim fixed the 1919 World Series.
So this character shows us that Gatsby is not what he seems and starts to hint at how Gatsby's American Dream has been gotten through crooked means.
The appearance of Meyer Wolfscheim, with his "tragic nose" as Nick remarks, underscores the fact that Gatsby is not one of the upper class. Since Wolfscheim obviously is a member of the Jewish mob that exists in New York, Gatsby's credibility as an Oxford man--or, "Oggsford," as Wolfscheim in his Yiddish accent pronounces it--is dashed after Nick Carroway meets him. Gatsby's connection with Wolfscheim also goes against the WASP elite's perception that men like Tom Buchanan have. No self-respecting East-Egger would be seen with a man such as Meyer Wolfscheim. Thus, the legitimacy of Jay Gatsby is questioned by Nick and others.