"... be kind to one another, tenderhearted,
forgiving one another,
just as God in Christ forgave you".
When people say, "I'm sorry", it's usually because they have affected a person, or persons, badly by actions or words, unintended or otherwise.
And, usually, trust had been violated and relationships broken.
In the best of situations a sincere apology is accepted and forgiveness is given with suitable words. Sometimes a promise no to do it again is included in the apology.
Ideally, the offence is cancelled. Normal, or the beginnings of normal, relationships can be renewed.
To forgive, then, is to verbally accept, from the heart, the sincere expression of regret and sorrow for the offence. That's human forgiveness.
Above all, Believers know God's forgiveness. It is given because He is merciful and in Christ Believers forgive others because of God's mercy to us: "... according to His mercy He saved us," Titus 3'5.
Here's a great example of His mercy:
"And you, being dead in your trespasses and the uncircumcision of your flesh, He has made alive together with Him, having forgiven you all trespasses," Colossians 2'13.
And that happened by His mercy and by His grace when Believers repented and received His Son.
Think of it, He takes unbelievers who are absolutely dead in sin and makes them absolutely alive in Christ's righteousness. Hallelujah!
(For more about forgiveness click Kingdom Praying 1&2 on the Menu.)