Substitutionary atonement

Technically speaking, substitutionary atonement is the name given to a number of Christian models of the atonement that all regard Jesus as dying as a substitute for others, 'instead of' them. It is expressed in the Bible in passages such as "He himself bore our sins in his body on the tree, that we might die to sin and live to righteousness", and "For Christ also died for sins once for all, the righteous for the unrighteous, that he might bring us to God." (although other ways of reading passages like this are also offered).

There is also a less technical use of the term "substitution" in discussion about atonement when it is used in "the sense that [Jesus, through his death,] did for us that which we can never do for ourselves".

There are a number of differing theories that come under the umbrella term "substitutionary atonement". The four best known are the Early Church Fathers' ransom theory; Gustaf Aulen's version of the ransom theory, called Christus Victor; Anselm of Canterbury's satisfaction theory; and the Reformed period's penal substitution theory. Care should be taken when one reads the language of substitution in, for example, Patristic literature, not to assume any particular substitution model is being used but should, rather, check the context to see how the author was using the language.

The ransom and Christus Victor theories present Jesus as dying to overcome (supernatural) powers of sin and evil. In this model, the devil has ownership over humanity (because they have sinned) so Jesus dies in their place to free them. The doctrine is that Jesus gave himself as a ransom sacrifice in behalf of the people. (Matthew 20:28) This is known as the oldest of the theories of the atonement, and is, in some form, still, along with the doctrine of theosis, the Eastern Orthodox Church's main theory of the atonement.

...
Wikipedia