The quick answer is that Jesus died on the cross to provide the way for us to receive forgiveness from our sins. The Bible provides many details regarding this sacrifice of Jesus. As we study the Bible, we understand more and more of salvation and forgiveness.
What does it mean that Jesus died for our sins?
When we say "Jesus died for our sins," we are saying that He died because of our sins. Sin leads to death (Romans 6:23). We were sinners consigned to death, and we had no way to stop sinning. Jesus came into our world and lived a perfect life, so death had no hold on Him. Yet, in His grace, Jesus chose to die on our behalf. He took our punishment for us. As He died "for our sins," as our substitute, He prayed that we would be forgiven. Since our penalty has already been paid, God will forgive all who put their trust in Jesus.
Jesus' death means that we have access to God. In John 14:6, Jesus says, "I am the way, and the truth, and the life. No one comes to the Father except through me." Sin had separated us from God, but, at the moment of Christ's death, the veil in the temple, separating the priests from the presence of God, was ripped in two (Mark 15:38).
Jesus' death means that the sacrifices of the Old Testament Law are no longer needed. In previous times, various offerings were required by the Law as atonements for sin. Yet these sacrifices were only temporary. With the sacrifice of Jesus, we were provided a perfect, one-time atonement from sin (Hebrews 10:10).
Christ's death means that we are guaranteed forgiveness of sin when we accept Jesus as Lord. Galatians 3:22 says, "the promise by faith in Jesus Christ might be given to those who believe." Jesus purchased our salvation on the cross by becoming sin for us (2 Corinthians 5:21). That is, He became the guilty one on our behalf.
Salvation is by God's grace through faith (Ephesians 2:8-9). It is made possible through the cross of Christ. "Christ also died for sins once for all, the just for the unjust, so that He might bring us to God" (1 Peter 3:18 NASB).
Is it true that Jesus is the only way to heaven?
How is Jesus the Lamb of God?
How is Jesus our mediator?
How is Jesus our High Priest?
Why should I believe in the resurrection of Jesus Christ?
Truth about Salvation