There are a number of "theories of atonement" in Christianity, and I don't know if this is the thread to necessarily get into all of them. But basic here is that Jesus, in joining with our suffering and death has released us from sin and death and reconciled us to God; the word "atonement" itself was coined by William Tyndale (16th century) as a combination of at-one-ment, or the state or condition of being at one with to translate a somewhat difficult to translate word/concept in the New Testament.
The idea here does not necessarily require that a payment be made to someone. However, if we are going to talk Atonement Theories, then an important one from early Christianity is Ransom Theory:
Ransom Theory, the most common view of the ancient Christian Fathers (along with Recapitulation Theory) states that humanity is held in bondage to the devil and the devil exercises his dominion over the world through death; Christ's death is a ransom payment made to the devil which releases human beings from the dominion of the devil, from the dominion of sin, death, and hell. Ransom Theory goes on to state that in this ransom payment the devil is, in a way, tricked; and the payment received (the crucified Jesus) is truly the devil's downfall. Christ's descent into Hades (the place of death) and resurrection means the overthrow of Hades, the defeat of the devil, and the ruination of death and sin.
So going by Ransom Theory, if there is something/someone that the "payment" is being made, it is as a ransom payment to the devil for the redemption and release of captives (us), and subsequently the total collapse and destruction of the devil's power and kingdom.
Understandably some are uncomfortable with the idea of God acting as a trickster or the idea that God would ever seemingly capitulate to the evil demands of the devil; but the basic idea here: That Christ's suffering and death has released the world from bondage and slavery to sin, death, hell, and the devil and to come into the freedom and peace of God is very much a centrally Christian idea regardless of Atonement Theory.
The point isn't that Jesus' blood is itself some kind of cosmic currency, but rather that blood signifies the pouring out of life--Jesus offering Himself and His life for the purpose of freeing, releasing, rescuing the world.
-CryptoLutheran