In The Scarlet Letter, what is a mythological and historical allusion?
Well, there are certainly plenty allusions for you to find! I will pick out one historical allusion for you and comment upon it, and hopefully this will give you the idea of how to work out what they mean, and above all, how Hawthorne is using them in this excellent novel.
At the end of Chapter 6, which concerns itself with the character of Pearl, Hester is thinking of the strange ways of Pearl and how some gossiping villagers insist that because the father has never been found she is the offspring of the Devil. Note how the author finishes this chapter:
Luther, according to the scandal of his monkish enemies, was a brat of that hellish breed; nor was Pearl the only child to whom this inauspicious origin was assigned, among the New England Puritans.
Luther here refers to the figure of Martin Luther, who was the leading figure in the Reformation in Germany. His revision of Christianity argued that salvation was to be won by faith rather than works. Here, then, this allusion allows Hawthorne to make an ironic comment on the Puritans belief that actually it was through works that they would be saved.