I often hear teachers instruct young people about what redemption means by giving the analogy of redeeming a coupon. While that is somewhat similar, Leon Morris in his book The Atonement: Its Meaning and Significance suggests that the meaning in antiquity had to to with deliverance.
In explaining what "redemption" means, he discusses three different word groups that are used in the Old Testament. The first one is g'l and it has a meaning related to family welfare. This is where the idea of "kinsman" comes from. We think of Ruth's "kinsman," Boaz, redeeming the field of Elimelech. The act is for preservation of family welfare.
The second word, pdh, carries with it an element of grace. Someone chooses to redeem another even though the captive may be left that way. The third word, kpr, is where the word "ransom," comes from, the money paid to deliver the one who is captive.
In all three cases, Morris points out that the deliverance is obtained at a cost to the deliverer. He uses that phrase "at cost," in relation to all three words. When applied to the New Testament and how Christ redeems us, the cost is Christ's suffering and death:
In the New Testament redemption is deliverance on payment of a price and when man's salvation is concerned that price is the death of the Son of God.
Morris goes on to say:
There is nothing automatic or axiomatic about redemption. Sinners have no reasons for expecting that they can ever be delivered from their sin and its eternal consequences. That Christ died for them is so wonderful that it is always to be received with awe and wonder. We, too, should pass our time in reverent fear, for our redemption is not a matter of silver or gold, or the like, but of the 'precious blood of Christ.'
We were captive to sin. A price was paid to deliver us; the ultimate price. And yes, that element of grace is there, that possibility that He could have left us right where we were. He did not.
To think of ourselves as captives who were delivered is a truth so amazing, we should with the hymn writer be crying out, "Redeemed, how I love to proclaim it!"