"Redeem" means "to buy out, especially of the purchase of a slave with a view to his freedom." It means "deliverance by Christ of Christian Jews from the Law and its curse." And "to release by paying a ransome price."
Our redemption is the work of the Lord Jesus Christ and His redeeming all of mankind from all iniquity (lawlessness; the bondage of self-will which rejects the will of God.)
Titus 2:14 AMP. says: "Christ Jesus gave Himself on our behalf that He might redeem us (purchase our freedom) from all iniquity."
Hebrews 9:12 AMP. states that Jesus went into the Holy of Holies in Heaven with His own Blood to make reconciliation between God and us.
His Blood and only His Blood secured our complete redemption ... the everlasting release from sin for us. This redemptive work brings deliverance to us through His death from the guilt and the power of sin.
Romans 3:24 speaks of the forgiveness, justification, and the deliverance that comes to us from the guilt of sins through the redemption that's in Christ Jesus.
Colossians 1:14 AMP.: "In Him we have our redemption through His Blood which means the forgiveness of sins."
This forgiveness of our sins includes both liberation from the guilt and doom of sin and introduction into a life of liberty.
This is the newness of life spoken of in Romans 6:4. We are to walk in this newness of life.
Reverend Robert W. & Mary C. Butler