When Mr. Wolfsheim meets Nick in a dark restaurant on 42nd Street, he tells Nick that Gatsby is an "Oggsford" man and that he has known him since the end of World War I. He also tells Nick that Gatsby is a man of fine breeding, handsome, a "perfect" gentleman, and the kind of person you could introduce to your mother and sister. Wolfsheim informs Nick that Gatsby is "careful" about women and would never look at a friend's wife.
As is so often the case with Gatsby, a fuller story comes out later. After Gatsby's death, Nick determinedly tracks Wolfsheim down about the funeral. Wolfsheim tells Nick that he met Gatsby when he was jobless and hungry. Gatsby had to wear his army uniform all the time because he couldn't afford any other clothes, and he hadn't eaten in several days. Wolfsheim says he fed Gatsby and, seeing his potential as an Oggsford man, apparently saw him as someone who could be used as a smooth, polished front for his illegal operations, and so he hired him. He says he "made" Gatsby.
Wolfsheim tells Gatsby nothing about Tom, but Tom does discuss Wolfsheim when he and Gatsby have their confrontation at the Plaza. Tom reveals he knows about the shady chain of "drugstores" Wolfsheim owned with Gatsby, doing his best to paint Gatsby as a criminal.
In a novel obsessed with class, being about Gatsby's attempts to transcend his own class, Wolfsheim's relationship with Gatsby further reveals the extent to which Gatsby came from nowhere. Wolfsheim is not a reliable character, but the basic contours of his story hold up, especially when confirmed by Tom's research and Gatsby's own admissions.