"To err is human, to forgive divine" means that everyone makes mistakes, but we should try to be like god and forgive one another. Divine basically means relating to, coming from, or like God or a god.
Divine also has an old-fashioned and informal meaning of being very good or pleasing, as in "She looked absolutely divine in her blue and white gown." This is an adjective that goes back to Middle English, borrowed from Old French devine, from Latin dīvīnus "divine, foreseeing," from dīvus "god."