forgiveness: the cancellation of the guilt and penalty of sin, God's pardon that lets the offense go and no longer counts it against the person
This is the standard word in the New Testament for forgiveness, and it is almost always paired with "of sins" or "of trespasses." It is built on a verb meaning "to send away, let go, release," so the picture underneath it is concrete: a debt is cancelled, a charge is dropped, a prisoner is let out. Forgiveness here is not merely a warm feeling that the offense no longer stings; it is a decisive release, an account closed for good.
That release is repeatedly tied to sacrifice. The blood of the covenant is poured out "for the forgiveness of sins" (Matthew 26:28), Hebrews states flatly that without the shedding of blood there is no forgiveness (Hebrews 9:22), and once forgiveness is granted, no further offering for sin is needed (Hebrews 10:18). In the letters it stands right beside redemption (ἀπολύτρωσις): believers have "redemption through his blood, the forgiveness of sins" (Ephesians 1:7). Redemption is the ransom that frees; forgiveness is the release from guilt that the ransom secures.
The word runs from the preaching of John, who called for "a baptism of repentance for the forgiveness of sins" (Mark 1:4), through the message the risen Jesus sends out to all nations (Luke 24:47), to the heart of the apostles' preaching (Acts 2:38; Acts 10:43). It is the pardon God offers, freely given yet grounded in the cross.