In the Old Testament, there are two primary Hebrew words which are translated as “pardon”, “pardoned” “forgive”, “forgiveness”, “forgiven” or “forgiving”. These are “nasa” and “salah”. Harris, Archer and Waltke say “nasa” means “the taking away, forgiveness or pardon of sin, iniquity and transgression. So characteristic is this action of taking away sin, that it is listed as one of God’s attributes (Exodus 34:7; Numbers 14:18, Micah 7:18)…Sin can be forgiven and forgotten, because it is taken up and carried away”.  Brown, Driver and Briggs say in Exodus 32:32, 34:7, Numbers 14:18, 1 Samuel 15:25, Job 7:21 and Micah 7:18, “nasa” means “take away guilt, iniquity, transgression etc., i.e. forgive”. 
Micah 7:18-19 contains these wonderful words: “Who is a God like you, pardoning iniquity and passing over the transgression of the remnant of His heritage? He does not retain His anger forever, because He delights in mercy. He will again have compassion on us, and will subdue our iniquities. You will cast all our sins into the depths of the sea.” This verse reveals that no angel or human has a character so willing to pardon wickedness done against Himself or others, as what God has.
Micah 7:18 says God delights in showing mercy. This means He enjoys doing it. He does not pardon our sins in a begrudging way. Verse 19 here shows how far God removes our sins from us – He figuratively hurls them into the depths of the sea.
When referring to the Hebrew word “salah”, Harris, Archer and Waltke say, “‘salah’ is used of God’s offer of pardon and forgiveness to the sinner. Never does this word in any of its forms refer to people forgiving each other”.  “Salah” is used in Exodus 34:9, Numbers 14:19-20, 2 Kings 5:18, 24:4, Psalm 25:11, Isaiah 55:7, Jeremiah 5:1, 5:7, 33:8, 50:20 and Lamentations 3:42.
Isaiah 55:7 reveals God requires humans to turn from their known sinful ways and thoughts to Him in order for their sins to be pardoned: “Let the wicked forsake his way, and the unrighteous man his thoughts; let him return to the Lord, and He will have mercy on him; and to our God, for He will abundantly pardon.”
Greek words for forgiveness or pardon
There are four main words used in the original Greek New Testament in relation to the forgiveness or pardon of our sins or crimes against God. These are the verb “aphiemi”, its associated noun “aphesis”, “charizomai” and “apoluo”.
The word “aphiemi” means “to send forth, send away, to remit or forgive debts and sins”.  Vine goes on to say that “aphiemi” “like its corresponding noun (aphesis), firstly signifies the remission of the punishment due to sinful conduct, the deliverance of the sinner from the penalty divinely, and, therefore righteously, imposed; secondly, it involves the complete removal of the cause of the offence; such remission is based upon the vicarious and propitiatory sacrifice of Christ”.  The word remission” means a cancelling or a release from something. The word “vicarious” means done on behalf of another or acting in place of someone. “Propitiation” means the removal of God’s anger against sinners and their sins.
Bauer says “aphiemi” means “cancel, remission of the guilt (debt) of sin…divine forgiveness”. 
There are numerous verses in the New Testament which use the word “aphiemi”. Romans 4:7, James 5:15, 1 John 1:9 and 2:12 are examples. Romans 4:7 relates to new creations in Christ: “Blessed are those whose lawless deeds are forgiven…” 1 John 2:12 is a wonderful statement of what happens when we receive Jesus as Lord and Saviour – our sins are forgiven or remitted: “I write to you, little children, because your sins are forgiven you for His name’s sake.” In the original Greek, the phrase “are forgiven” is in the perfect tense. The perfect tense either means God forgave us all our sins and this has continuing effects in our lives or we are in a state of having been forgiven.
1 John 1:9 reveals how Christians can obtain complete remission or forgiveness of any sins they may fall into after conversion. 1 John 1:9 states: “If we confess our sins, He is faithful and just to forgive us our sins and to cleanse us from all unrighteousness.” When this verse says God is faithful, it is referring to His faithfulness to His New Covenant promises to forgive believers of their sins. When this verse declares God is just, it means He forgives believers’ sins in ways that are in agreement with His perfect justice. In other words, He forgives because Jesus has taken the punishment owing to God’s perfect justice because of our sins.
The word “aphesis” means “pardon, cancellation of a…punishment or guilt, forgiveness of sins.”  “Aphesis” is used in Matthew 26:28, Mark 1:4, Luke 1:77, 3:3, 24:47, Acts 2:38, 5:31, 10:43, 13:38, 26:18, Ephesians 1:7, Colossians 1:14, Hebrews 9:22 and 10:18. Acts 13:38 states this forgiveness or remission of sin is through Jesus Christ.
Ephesians 1:7-8 shows this forgiveness of sin is totally by undeserved unmerited grace through the purchase price of Jesus’ physical death: “In Him we have redemption through His blood, the forgiveness of sins, according to the riches of His grace…” Colossians 1:14 speaks similarly.
Acts 26:18 associates receiving this remission or forgiveness of sin with having a personal faith in the Lord Jesus Christ: “…that they may receive forgiveness of sins and an inheritance among those who are sanctified by faith in Me.” Acts 2:38 links repentance or having a change of heart about God, Christ and our known sins to the type of conversion that receives full remission or forgiveness of sins.
In the original Greek, Colossians 2:13 uses a form of the word “charizomai” in the phrase which speaks of God “…having forgiven you all trespasses…” The Greek word “charizomai” means in the context of Colossians 2:13 “give – equalling remit, forgive, pardon”  or in the context of Luke 7:42 means “to release a person from the obligation of repaying what is owed”.  In Luke 7:42, Jesus spoke of a creditor freely forgiving two debtors their debts. Here Jesus compares forgiveness of sin to freeing a person from their responsibility to pay their debts. Because the word “charizomai” is derived from the word “charis” which means God’s freely given grace, this reveals forgiveness of sin is a totally free, unmerited act of God’s grace or kindness.
“Apoluo” is another word used in the original Greek New Testament for forgiveness or pardon. “Apoluo” means “set free, release, pardon a prisoner…release a debtor”.  This word is used in Luke 6:37: “…Forgive, and you will be forgiven.”
Most of the usages of “apoluo” in the New Testament relate to the legal releasing or pardoning by Governor Pontius Pilate of Barabbus, the condemned criminal or to Pilate’s consideration of legally pardoning or releasing Jesus from His assumed “crimes”. These references are found in Matthew 27:15, 17, 21, 26; Mark 15:6, 9, 11, 15; Luke 23:16, 18, 20, 22, 25; John 18:39; 19:10, 12; and Acts 3:13.
In Matthew 18:21-35, Jesus teaches about forgiveness of sins or debts. In Matthew 18:27, “apoluo” is used also in relation to a servant being released by a king after having a debt cancelled: “Then the master of that servant was moved with compassion, released him, and forgave him the debt.” In Greek, the word “released” here is a form of “apoluo” and “forgave” is a form of “aphiemi”. In this parable, “apoluo” relates to our having a great debt owing to God our Supreme King and Judge Who in loving compassion and mercy cancels our debt and then lets us go free. Verse 27 refers to the King’s compassion and verse 33 mentions the King’s mercy. Also note verses 23 and 24 refer to the king settling accounts with his subjects.
Matthew 18:24 says the man’s debt was ten thousand talents. This is equivalent to millions of dollars. No slave in ancient times could ever repay such a debt. People in ancient times would understand this comparative amount far better than modern Westerners. This is just like us. We owe God an unpayable debt. But in mercy, God cancels our debt, forgives us and lets us go free. God does all this perfectly legally on the basis that Jesus Christ has paid the unpayable debt for us.
Louw and Nida say “aphiemi”, “aphesis” and “apoluo” all mean “to remove the guilt resulting from wrongdoing…It is extremely important to note that the focus in the meanings of ‘aphiemi’, ‘aphesis’ and ‘apoluo’ is upon the guilt of the wrongdoer and not upon the wrongdoing itself. When God forgives the wrongdoer, the event of wrongdoing is not undone, but the guilt resulting from such an event is pardoned. To forgive, therefore, means essentially to remove the guilt resulting from wrongdoing”. 
 Harris, Archer and Waltke, page 601.
 Brown, Driver and Briggs, page 671.
 Harris, Archer and Waltke, page 626.
 Vine, page 250.
 Bauer, page 125.
 Ibid, page 185.
 Ibid, page 876.
 Louw and Nida, pages 582-583.
 Bauer, page 96.
 Louw and Nida, page 503.