Jesus Christ suffered the penalty for our sins so that we can repent. Repentance is a change of heart and mind that brings us closer to God. It includes turning away from sin and turning to God for forgiveness. It is motivated by love for God and sincere desire to obey His commandments.
Why is it even necessary to repent and how can it help me?
We all sin, no matter how hard we try. Jesus is the only being who has not sinned. Yet we are commanded to be perfect, even as our Father in Heaven is perfect, to return to the kingdom of God. Sin also carry's a heavy emotional burden on each of us. So how can anyone, since we are all imperfect return to God and feel free of sins heavy burden? Through repentance. God is a both a merciful and a just God. We must be punished for our own sins according to justice, but to be merciful he sent his Son Jesus Christ to suffer for us in our place. We can only be forgiven through repentance. This is why it is so important! "He suffered and died for our sins, but without repentance all of his anguish and pain on our account are futile." (The Miracle of Forgiveness, p 145)
This video below does an amazing job of explaining what the atonement is for. It portrays of the analogy Elder Boyd K Packer used in his April 1977 conference address of a young man who fails to pay his debt (representing sin) and is saved from the grasp of justice (the punishment of God) through the mediations of a friend (Jesus Christ).
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