Words related to the practice of ransoming are often found in discussions of Christian redemption ('redemption' being such a word). People seem somewhat skittish about it, however; you find critics, for instance, of 'the ransom theory of atonement'. There is no 'ransom theory of atonement', just a common tendency, rooted in the Scripture and the Fathers, to talk about redemption in terms of ransoming, but it's interesting that people would have such a problem, given that it is easily one of the best-founded ways of talking. We have Jesus, for instance:
For the Son of Man came not to be served but to serve and to give his life a ransom for many. (Mk 10:45 NRSV)
Or St. Paul:
For there is one God; there is also one mediator between God and humankind, Christ Jesus, himself human, who gave himself a ransom for all. (1 Tim. 2:5-6 NRSV)
To take just two obvious ones.
There are also several features of ransoming as a practice that make sense of redemption.
(1) Ransom is an exchange in which there is no right to demand or duty to pay. In ordinary commercial exchanges, I have a commodity or can offer a service by right, then I give you this commodity or service, which creates a duty to pay in you, which gives me a right to demand from you. Ransoming a captive is not a commercial exchange in this way. The captor has no particular right to the person in question; nor does he have a right to offer a person as a commodity; nor does he have the right to offer delivery of the person as a paid service. If the prisoner were to get away somehow, the captor's rights would not have been harmed by the prisoner. All the captor has, is physical possession. Likewise, the ransomer has no duty to pay the captor. There might be situations where he has a duty to ransom that springs from something else entirely, but it's never going to be a duty to the captor.
(2) Thus the ransoming is grounded not in a duty to pay but in a mercy; there is a reason why ransoming captives is a traditional act of mercy or almsdeed. What grounds the mercy to pay is in fact just the need of the captive. Ransoming is not an act of justice to captors; it is an act of mercy to captives.
(3) However, this does not mean that justice is not relevant here. When the ransomer pays, they do get the right to demand the release of the captive; if a captor receives the ransom payment and refuses to release the captive, this is a further injustice beyond any that may have been committed up to that point. Thus, once the ransom has been given, the captor has a duty to deliver arising from the ransomer's right to receive.
(4) Having been ransomed, the ransomed captive incurs a duty of gratitude to the ransomer as benefactor.
Points at least closely related to all of these are all essential to the Christian doctrine of redemption. God has no duty to redeem us; He acts out of mercy. What He redeems is redeemed, and nothing has a right to interfere with that. And the redeemed have duties of gratitude to their Redeemer.
Perhaps one of the reasons people are skittish with it is the question of the captor. As the Catholic Encyclopedia article has it:
When a captive is ransomed the price is naturally paid to the conqueror by whom he is held in bondage. Hence, if this figure were taken and interpreted literally in all its details, it would seem that the price of man's ransom must be paid to Satan. The notion is certainly startling, if not revolting. Even if brave reasons pointed in this direction, we might well shrink from drawing the conclusion. And this is in fact so far from being the case that it seems hard to find any rational explanation of such a payment, or any right on which it could be founded.We can already be clear on one point -- there is no right on which it is founded. Captors have no right to either the captive or the payment; they just have the captive.
A somewhat stronger argument is given by St. Gregory Nazianzen (Oration 45.xxii):
We were detained in bondage by the Evil One, sold under sin, and receiving pleasure in exchange for wickedness. Now, since a ransom belongs only to him who holds in bondage, I ask to whom was this offered, and for what cause? If to the Evil One, fie upon the outrage! If the robber receives ransom, not only from God, but a ransom which consists of God Himself, and has such an illustrious payment for his tyranny, a payment for whose sake it would have been right for him to have left us alone altogether.
But any shame would be on the part of the captor, not on the part of the ransomer or the ransomed. St. Gregory of Nyssa in his own discussions of ransom, argues that the fact that we are voluntarily complicit in our own oppression means that justice prevents us from being simply torn away by force; thus God instead takes a different route (Catechetical Oration c. 22):
[N]ow that we had voluntarily bartered away our freedom, it was requisite that no arbitrary method of recovery, but the one consonant with justice should be devised by Him Who in His goodness had undertaken our rescue. Now this method is in a measure this; to make over to the master of the slave whatever ransom he may agree to accept for the person in his possession.We might put the point a little more broadly than this, by noting that even though the captor has no right to demand payment, there can still be reasons why ransom would be better than forcible liberation, and one of those reasons is that it might be better for the captive. And just as the police might pay a ransom in order simultaneously to free a captive and catch the captor in a legal bind, so, St. Gregory of Nyssa thinks, God has done in our case (Catechetical Oration 23):
The Enemy, therefore, beholding in Him such power, saw also in Him an opportunity for an advance, in the exchange, upon the value of what he held. For this reason he chooses Him as a ransom for those who were shut up in the prison of death. But it was out of his power to look on the unclouded aspect of God; he must see in Him some portion of that fleshly nature which through sin he had so long held in bondage. Therefore it was that the Deity was invested with the flesh, in order, that is, to secure that he, by looking upon something congenial and kindred to himself, might have no fears in approaching that supereminent power; and might yet by perceiving that power, showing as it did, yet only gradually, more and more splendour in the miracles, deem what was seen an object of desire rather than of fear. Thus, you see how goodness was conjoined with justice, and how wisdom was not divorced from them.
This is sometimes called "the fishhook" because St. Gregory later goes on to compare this to God baiting a hook and catching the devil with it. He makes clear that this is in a sense a kind of turnabout: the devil caught us by baiting a trap, the semblance of good baiting the hook of evil, so God catches the devil with another baited hook, taking advantage of the devil's greed for more. God gives the devil a taste of his own medicine (and, in fact, St. Gregory uses exactly this imagery, noting that both a doctor and a poisoner may use the same drug because what matters is the use to which it is put). The imagery, of course, comes from Job 41:1, in a rhetorical question contrasting what a man can do and what God can do: "Can you draw out Leviathan with a hook?" The imagery was quite popular among the Fathers.
Essentially the same account, however, can be found without the fishhook in St. Irenaeus (Adv. Haer. 5.1.1):
And since the apostasy tyrannized over us unjustly, and, though we were by nature the property of the omnipotent God, alienated us contrary to nature, rendering us its own disciples, the Word of God, powerful in all things, and not defective with regard to His own justice, did righteously turn against that apostasy, and redeem from it His own property, not by violent means, as the [apostasy] had obtained dominion over us at the beginning, when it insatiably snatched away what was not its own, but by means of persuasion, as became a God of counsel, who does not use violent means to obtain what He desires; so that neither should justice be infringed upon, nor the ancient handiwork of God go to destruction.
What happens if you accept God as payment in order to release something to which you had no particular right? You now have an infinite debt, and the one who paid has an infinite right to demand, one about which you have no right at all to complain.
This is, of course, in no way a complete account; it's just sufficient to make sense of why we can talk about Christian redemption in terms of ransom. It's often said that St. Anselm rejects the 'ransom theory' in Cur Deus Homo, but in fact the character who raises the objection in that work (which is essentially the one raised by Catholic Encyclopedia) is not Anselm but Boso, and it's clear in Anselm's response that St. Anselm takes his discussion of satisfaction to fill the gaps in talking about the redemption in terms of ransom, rather than replacing such talk altogether. And so it would be with any other account.