To redeem means "to buy back." It has the thought of deliverance upon payment of a ransom.
As sinners, we are captives of sin and the devil. We are totally helpless, of ourselves, to be reconciled to God. The Lord Jesus Christ, through His Death on the Cross, paid the debt, (or the ransom price) to bring guilty sinners back to God - to set them free, and deliver them from sin and its penalty.
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"He paid a debt He did not owe, I owed a debt I could not pay,
I needed someone to wash my sins away.
And now I sing redemption's song, 'Amazing Grace.'
Christ Jesus paid a debt that I could never pay.”
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" In Whom (ie the Lord Jesus) we have Redemption through His Blood, even the forgiveness of sins....” (Colossians 1:14)
"... he is a rewarder of them that diligently seek him" Hebrews 11:6