Originally, the word redemption meant the payment of a price to secure the release of a prisoner of war. Israel were redeemed by God out of slavery in Egypt. And the New Testament takes up that story and says that it was merely a physical illustration of the spiritual redemption that was to come. The Old Testament tells us how through the sin of Adam and Eve humanity sold itself into slavery to sin. The New Testament tells us that in Jesus Christ, God bought us back, or redeemed us, from slavery to sin and from the curse of the Law which condemns sin.
Redemption always means the payment of a price to secure release.
It was the blood of Jesus Christ, the Son of God, shed for us at the cross as an atonement for sin. Now this passage tells us that Christians have been redeemed, it tells us who has redeemed us, and it tells us what we have been redeemed from and why we have been redeemed. The bible is absolutely clear that no one can redeem themselves. Not spiritually anyway. In the Old Testament, and in Roman and Jewish law, a slave could buy his own freedom if he somehow managed to earn enough money to do so.