Rowan Williams (Sign and Sacrifice) summarizes the Anselmian understanding of the atonement using the categories of sacrifice, obedience, and gift, all set within a Trinitarian frame. It's quite lovely.
Citing Hebrews citing Psalm 40, Williams argues that the Old Testament sacrificial system existed to symbolize the true sacrifice of obedience. Obedience is pleasing to God because it is “a reflection of his own love, his glory and his beauty.” Obedience isn't duty-doing but “a harmony of response to God so that God sees in the world a reflection of his own life. Our actions in obedience reflect his.” This is what God loves to see, “his selfless love reflected, to see his beauty mirrored back to him.” A perfect sacrifice, a perfect return gift, is “the return to him of his own wholly generous love.”
Obedience is the mode of Jesus' whole life, so that “in Jesus there is the divine action of love mirrored back to God through the medium of a human life.” This leads Williams from a meditation on sacrifice “right into the middle of the doctrine of the Trinity and the doctrine of the Incarnation. Our language about sacrifice has shown us a God who is giving and receiving and responding. This is a God who pours out love and draws it back: a God who is himself relationship, not a solitary tyrant waiting for us to get on the right side of him.”
Jesus' obedient sacrifice in death brings us into His relationship with His Father: “the Father pouring out his love, the Son watching what the Father is doing and playing it back to him, the Spirit enabling us to share that response to the Father, watching and loving.” That eternal dynamic of life and love is enacted on earth in the life of Jesus. In Him “we see all of that vast infinite eternal reality happening in a human life, happening in a weary, dusty-footed unkempt man completing a long journey, sitting down with his friends at the end of the day, breaking bread and pouring wine.”
In the cross, “what we see is no less than the Holy Trinity: the life of God poured out, the life of God reflected back in love from the earth and the breathing of that life freely to the ends of creation, the Spirit of Jesus.” In that gift of utter obedience, which mirrors the Father's love back to the Father, Jesus “changes the definition of what human beings are. It interposes between God and human failure, a new face for humanity.”
And we, whose faces are shamed by our sin, can present the face of Christ to the Father. We can say, ”You know that humanity is more than me and my miserable and wretched and incompetent struggles to be human, because you have given to the world perfect humanity: Jesus’ humanity.” In Christ, we present an image of the Father back to the Father, the new face of humanity.