Yea, many there be that have that have run out of their wits for women, and become servants for their sake. Many have perished, have erred, and sinned for women…O ye men, how can it be but women should be strong, seeing they do thus? – Esdras
This is a quote from the First Book Esdras in the Apocrypha (learn more about the Apocrypha). For our purposes, the Epigraph sets up two things. The first is that we get an idea of what might happen to Jude along the way through the novel. Ultimately, he does err, sin, and perish for women.
Secondly, the epigraph shows how foolish men are to think that women are somehow the "weaker" sex. Remember, at one point in the novel Sue's bed and the bed of her fellow female students are all adorned with the words "The Weaker." (3.3.8). (Ew, creepy much?)
This epigraph reminds us that, if men are willing to do all these crazy things for women, women must be pretty strong after all.