For Christ also suffered once for sins, the righteous for the unrighteous, that he might bring us to God, being put to death in the flesh but made alive in the spirit.
1 Peter 3:18
This is a clear, concise statement of the substitutionary atonement of Jesus. When Jesus died on the cross, he died in our place. He died in my place. He died in your place.
He died as our substitute. The righteous died for the unrighteous, so that we might become righteous, or right with God.
In his superb book, Center Church, Tim Keller writes about the various images of atonement in the Bible and how substitution is the key idea behind all of them.
But perhaps the single most consoling and appealing theme is what theologian Roger Nicole has called the one, irreducible theme that runs through every single one of these models – the idea of substitution. Dr. Nicole taught that, regardless of the grammar being used, the essence of the atonement is always Jesus acting as our substitute. Jesus fights the powers, pays the price, bears the exile, makes the sacrifice, and bears the punishment for us, in our place, on our behalf. In every grammar, Jesus does for us what we cannot do for ourselves. He accomplishes salvation; we do nothing at all. And therefore the substitutionary sacrifice of Jesus is at the heart of everything.