Philosopher Merold Westphal says that guilt is a mode of self-consciousness. You know you've done the wrong thing, you're ashamed and you have a sense you deserve punishment. The picture of Jesus' death as a sacrifice helps us understand how his death deals with our guilt.
In his novel The Plague, Albert Camus says that our common human experience is one of suffering and exile longing for love. Through Jesus' reconciling work on the cross, God brings us exiles home.