"Do you forgive me?"
Translation:Vergibst du mir?
“Me” can mean either mich or mir. The difference between these forms is their grammar case. Mir is DATIVE personal pronoun and mich is ACCUSATIVE personal pronoun. There are specific verbs that match with dative and verzeihen/vergeben is one of them! You can find an online list with this kind of verbs, they are called dative-verbs. Have a nice Evening