The word 'atonement' is used as the term regarding what Christ did on our behalf by His death and resurrection to free us from sin and Satan. Theories of the atonement try to explain exactly how that atonement was accomplished.
The most common theory of atonement is what is called Penal Substitution. The idea is that Jesus satisfied the demands of justice by suffering for our sins, thereby relieving us of sin's penalty. This means that God was justifiably angry at our sin and that it must be punished. Jesus took our place in judgment so that we could be justified. I think that most of us agree on that. It is standard evangelical teaching.
But there was a theory, dominant in the church for many centuries, called the Ransom-to-Satan theory. It said that our sin put us in bondage to Satan and that Jesus, by his sacrifice, bought us out of this bondage. Jesus defeats Satan and frees us. Jesus' sacrifice is, then, a kind of ransom paid to Satan rather than a satisfaction of divine justice.
Now to many of us this will seem to be a strange theory not even worth considering as a proper theory of atonement. But I would caution the church not to throw out the baby with the bath water. I certainly do think that it is mistaken to consider Christ's sacrifice as a ransom paid to Satan, but there is something here that we will miss if we are not careful. The idea that Satan has mankind in bondage and that he must be freed is quite scriptural. Let's look at some scripture:
Hebrews 2:14-15 "Since the children share in flesh and blood, He Himself likewise also partook of the same, that through death He might render powerless him who had the power of death, that is, the devil,and might free those who through fear of death were subject to slavery all their lives."
Colossians 2:13-15 "When you were dead in your transgressions and the uncircumcision of your flesh, He made you alive together with Him, having forgiven us all our transgressions,having canceled out the certificate of debt consisting of decrees against us, which was hostile to us; and He has taken it out of the way, having nailed it to the cross. When He had disarmed the rulers and authorities, He made a public display of them, having triumphed over them in it."
It sure looks to me like Jesus in His atoning work defeated Satan as well as satisfying the demands of justice. Our transgressions are forgiven because our debt is satisfied. Then Jesus disarms (spoils) the demonic powers freeing us from bondage. But some would have you to believe that this is not necessary. All that is needed is forgiveness of sins.
Apparently, forgiveness of sins alone is not enough to free us from Satan. Satan must be personally defeated. And that is what Jesus did after He had finished satisfying the demands of justice.
Here is a natural illustration: Suppose someone offends a king and part of his punishment is banishment. He goes to another country where the ruler puts him in chains. But the king wants his old subject back, but not without punishment for his sins. The king then allows another to take his place in judgment. Another will suffer in the offender's place. The substitute suffers on the offender's behalf. Wonderful! Can the former-offender go back home now? No. He is still in bondage. The substitute (or someone else) must defeat the ruler of the other country. Only then is the former offender truly free.
Too often in the church we are led to believe that if we accept one idea that we must reject another. This is not always the case. We need to study all ideas and keep the parts that are true of each theory and discard the rest. We certainly do need to make the idea of penal substitution the centerpiece of our atonement theology. However, we must often blend ideas together to explain all the biblical evidence. We must be careful not to adopt an 'either-or' mentality.