To give graciously, to bestow as a favor, to forgive a debt or offense. From charis (grace), charizomai means giving that flows from generosity, not obligation. It covers both gift-giving and debt-canceling, both grace and forgiveness.
God graciously gives us all things (Romans 8:32): salvation is a gift, not wages. Paul uses charizomai for forgiveness: 'forgiving each other, as God in Christ forgave you' (Ephesians 4:32). The parable of the two debtors (Luke 7:42) uses this verb — both debts were graciously canceled. Forgiveness is not minimizing offense but absorbing the cost and releasing the debtor. God's forgiving mirrors His giving — both are grace.