Why does forgiveness set people free?

32 Be kind to one another, tenderhearted, forgiving one another, as God in Christ forgave you. Ephesians 4:32 (ESV)

Now the birth of Jesus Christ took place in this way. When his mother Mary had been betrothed to Joseph, before they came together she was found to be with child from the Holy Spirit. 19 And her husband Joseph, being a just man and unwilling to put her to shame, resolved to divorce her quietly. 20 But as he considered these things, behold, an angel of the Lord appeared to him in a dream, saying, “Joseph, son of David, do not fear to take Mary as your wife, for that which is conceived in her is from the Holy Spirit. 21 She will bear a son, and you shall call his name Jesus, for he will save his people from their sins.” Matthew 1:18–21 (ESV)

Jesus is the gift of forgiveness.

“For unto you is born this day in the city of David a Savior, who is Christ the Lord.” Luke 2:11 (ESV)

“…to give knowledge of salvation to his people in the forgiveness of their sins…” Luke 1:77 (ESV)

“God exalted him at his right hand as Leader and Savior, to give repentance to Israel and forgiveness of sins.” Acts 5:31 (ESV)

“Of this man’s offspring God has brought to Israel a Savior, Jesus, as he promised.” Acts 13:23 (ESV)

“And though they found in him no guilt worthy of death, they asked Pilate to have him executed.” Acts 13:28 (ESV)

How does God save us? How does Jesus forgive us?

11 But when Christ appeared as a high priest of the good things that have come, then through the greater and more perfect tent (not made with hands, that is, not of this creation) 12 he entered once for all into the holy places, not by means of the blood of goats and calves but by means of his own blood, thus securing an eternal redemption. 13 For if the blood of goats and bulls, and the sprinkling of defiled persons with the ashes of a heifer, sanctify for the purification of the flesh, 14 how much more will the blood of Christ, who through the eternal Spirit offered himself without blemish to God, purify our conscience from dead works to serve the living God. 15 Therefore he is the mediator of a new covenant, so that those who are called may receive the promised eternal inheritance, since a death has occurred that redeems them from the transgressions committed under the first covenant. Hebrews 9:11–15 (ESV)