Redemption was a word used by the first-century Roman world. And the writers of the New Testament adopted that word to describe what Jesus did for us on the cross. In the secular world of the day, redemption had to do with slavery. In particular, the purchase of freedom for a slave.
For you know that it was not with perishable things such as silver or gold that you were redeemed from the empty way of life handed down to you from your ancestors, but with the precious blood of Christ, a lamb without blemish or defect. (1 Peter 1:18-19 NIV)
The New Testament pictures us as being in bondage to sin, enslaved to our sinful natures. But we have been redeemed from that slavery to sin and set free from its bondage. However, there was a cost to that redemption. And the price was much greater than for the redemption of a slave. Rather than silver or gold, the typical redemption price for a slave, the cost of our redemption was the blood of Jesus, shed for us on the cross.
Peter’s purpose in relating the cost of our redemption was not simply to satisfy our curiosity. Instead, this follows his call to us not to conform to the evil desires of our past life (1 Pet. 1:14); to be holy in all we do (1 Pet. 1:15); and to live our lives here as foreigners in reverent fear (1 Pet. 1:17). The Father paid a high price for our redemption, the life of his Son. And, because of that, he expects much from us (1 Pet. 1:17). Because of the price paid for my redemption, it is only reasonable that I give myself fully and completely to him.