The Moral Influence Theory of the Atonement was developed by a French theologian/philosopher named Peter Abelard (1079-1142). He has been described as extremely charismatic and the most outstanding theologian of the twelfth century.(Google his name. He really was an interesting fellow).
Abelard would say, with others, that Jesus was obedient unto death. He knew that a premature death would be his destiny because of what he was saying and doing which manifested itself as a threat to the power of Rome and the religious elite of the day. His death had nothing to do with the defeat of Satan or the satisfaction of God's need for justice. This theory reflects a change in disposition, not of God or Satan, but rather humanity.
The purpose of the death of Jesus, according to Abelard, was to provide an example for humanity to follow. His was a willingness to suffer whatever it took, including death, in order to show the love of God for everyone. Regardless of what humanity did to him, Jesus was willing to absorb the rejection and pain, and still love. By doing so, he was stating that this is the image of God. God is not a petty despot who needs satisfaction. God loves regardless.
Another point that would be made with this theory is the idea that though Jesus was crucified by human hands, it must be said that God is God and there is no other. God is God and Caesar is not, even though Caesar could made the call to execute.
The hoped-for end result is that human beings would learn to love like that......absorb the pain, reaction and rejection, but still keep on loving.
This is a position held by some folk who are more liberal. As one can imagine, this theory has received much attack and denigration.
Next, I will go to more contemporary theories of atonement. And I will attempt to conclude with what I think was Jesus' take on this whole matter.