Atonement is central to what Christians believe. Yet, many believers cannot define this important word. Michael Horton offers this explanation, “Christ died in our place, bearing God’s wrath, satisfying his justice, and reconciling us to the Father.”
Broadly, the word “atonement” refers to reparation for an offense. In the context of Christianity, the wrong in view is the rebellion of all image bearers against our Creator and the reparation is the reconciling of God and humanity through the work of God’s only unique Son, the Lord Jesus Christ (2 Cor 5:21). So Jesus atoned for the sins of Christians.
But how did Jesus atone for the sins of his people? The Bible teaches that the atoning work of Christ involves both substitution and satisfaction. Christ was the substitute for his people and he satisfied the demands of God’s justice (1 John 4:10, Isaiah 53, 2 Cor 5:21).
Said another way, the central aspect of Christ’s atoning work is that that he paid the penalty for his people on the cross. Theologians refer to this truth as penal substitutionary atonement. Michael Horton summarizes, “Christ died in our place, bearing God’s wrath, satisfying his justice, and reconciling us to the Father.”
In order that we might grasp both the problem sin creates, and the solution for how sinners can be right with God, the Bible describes sin using different pictures including debt, enmity, and crime. R.C. Sproul helps us understand how Christ atones for our sin with the following table.
|Sin as . . .||Man||God||Christ|
For more, see Kevin DeYoung’s important post, Substitution is Not a “Theory of the Atonement”
 R.C. Sproul, Essential Truths of the Christian Faith (Wheaton: Tyndale House, 1992), 172–173.
 Michael Horton, Pilgrim Theology: Core Doctrines for Christian Disciples (Grand Rapids: Zondervan, 2011), 208.
 R.C. Sproul, The Truth of the Cross (Orlando: Reformation Trust, 2007), 42.