Occasionally stories are told about someone being sentenced for a crime when suddently another person steps up and says, "I will take the punishment for him." Most stories are not based in fact. But the New Testament teaches that Jesus, in His death, has talen the penalty for our sin upon Himself.
Scripture teaches that all humanity is tainted and corrupted by sin, both because of the sin of our forefather Adam (Romans 5:12-21) and because we ourselves are all sinners (Ephesians 2:1-3). God, as the righteous judge, cannot and will not simply overlook sin, since sin violates His nature and brings destruction to the perfect world He created. God would be unjust simply to say, "Oh well, boys will be boys." Instead, sin must be punished, and since all of us have broken God's law, we rightly deserve full punishment. Yet, amazingly, Jesus came to take our punishment upon Himself.
The New Testament speaks of Jesus' death providing forgiveness in at least three ways. First, Jesus' death was a sacrifice for our sins. Christ fulfills the Old Testament sacrifical system in being both high priest and sacrifice (Hebrews 5-10). On the Day of Atonement, animals were killed before the altar and the blood was sprinkled on the mercy seat in the most holy place. Under that seat were tablets of stone upon which had been written the Ten Commandments. Looking down from Heaven God could see the law, but when the sacrifical blood was sprinkled, the law---as reminder of the people's sin---was covered. Without the shedding of blood, there is no forgiveness of sin )Hebrews 9:22).
Second, the New Testament speaks of Christ's death as a "propitiation" for our sin (Romans 3:21-26). This word, hilasmos, carries the meaning of "an offering sayisfying God's wrath toward sin," yet remarkably god Himself provides this offering. When Jesus died on the cross, He cried out, "My God, My God, why have you forsaken Me?" (Matthew 27:46). The Father was pouring out His wrath because "He made the One who did not know sin to be sin for us, so that we might become the righteousness of God in Him" (2 Corinthians 5:21).
Third, and related to both points already made, the Bible speaks of Christ's death as a substitution. Jesus did not come to be served but to serve and "to give His life---a ramson for many" (Mark 10:45). Jesus "gave Himself for our sins to rescue us from this present evil age" Galatians 1:4). Isaiah's predictions of a coming Suffering Servant are fulfilled in the death of Jesus, who "was pierced because of our transgressions, crushed because of our iniquities...and the Lord has punished Him for the iniquity of us all" (Isaiah 53:5-6). He died in our place.
By faith, and faith alone, we receive the forgiveness Christ provides through His humiliating and painful death. The result? Eternal life (Ephesians 2:3-10).
Reference:Apologetics Study Bible, author:Chad Owen Brand