Origins
The word 'forgive' is one of the clearest examples of a calque (loan-translation) in the history of the English language. It comes from Old English 'forġiefan' (to give up, to give away, to allow, to pardon), from 'for-' (completely, away, forth) + 'giefan' (to give), from Proto-Germanic *fra-gebaną (to give away). The word was formed as a direct translation of Latin 'perdōnāre' (to give completely, to forgive), from 'per-' (through, completely) + 'dōnāre' (to give, to donate). The Germanic and Latin words mirror each other exactly: for- = per- (completely); give = donate (to give). To forgive is to give away — to release one's claim to anger, to surrender one's right to punish.
The same process occurred independently across the Germanic languages. German 'vergeben' (ver- 'away' + geben 'to give'), Dutch 'vergeven' (ver- + geven), and Gothic 'fragiban' (fra- + giban) all translate the same Latin structure with native Germanic materials. This parallel development reveals the profound influence of Christian Latin on early Germanic languages, as missionaries translated the concept of divine forgiveness into local vocabulary.
The Latin original 'perdōnāre' took its own path through the Romance languages, producing French 'pardonner' and Italian 'perdonare,' which entered English as 'pardon' in the thirteenth century. So English possesses both sides of the calque: the Germanic 'forgive' and the Romance 'pardon' — two words expressing exactly the same metaphor (complete giving-away) in two different linguistic registers. In modern usage, 'forgive' tends to be more personal and emotional (forgiving a friend's betrayal), while 'pardon' is more formal and legal (a presidential pardon, 'pardon me').
Old English Period
The prefix 'for-' in Old English is not the same as the preposition 'for.' It is an intensifying or privative prefix meaning 'completely, away, to destruction' — the same prefix that appears in 'forbid' (to completely prohibit), 'forget' (to completely lose from the mind), 'forsake' (to completely abandon), and 'forgo' (to completely do without). In each case, 'for-' adds a sense of totality or finality to the base verb.
The economic metaphor embedded in 'forgive' is not accidental. In both ancient and modern usage, debts can be 'forgiven' — a lender forgives a debt by giving up their right to repayment. The Lord's Prayer makes this connection explicit: 'Forgive us our debts, as we forgive our debtors' (Matthew 6:12). The parallel between moral and financial forgiveness reveals an ancient understanding of wrongdoing as incurring a debt — the wrongdoer owes the wronged party something (punishment, restitution, an apology), and forgiveness is the cancellation of that debt.
The relationship between 'forgive' and 'gift' is direct: both derive from Proto-Germanic *gebaną (to give). To forgive is to give away; a gift is something given. Forgiveness is, etymologically, the greatest gift — the giving away of one's right to revenge.