The Black Man is a euphemism for Satan in this book: Hester considers the scarlet letter A to be the Black Man's mark, and Pearl wonders aloud if the Black Man left his brand on Dimmesdale's heart. Our narrator loves to compare Chillingworth to Satan as well.
By invoking Satan, our narrator raises the question of whether humans are innately good or evil, and whether they truly choose to be evil—to write their names in the Black Man's book, or become "enticed […] into a bond that will prove the ruin of [their] soul" (4.33)—or whether evil happens by accident, like Hester and Dimmesdale's love affair. The Puritans definitely like to use the Black Man as a symbol of all evil, making evil something separate from common human life. But we're not so sure that Hawthorne agrees.