He writes: "In the encyclical Deus Caritas Est, I dwelt upon this theme of love highlighting two fundamental forms: agape and eros. The term agape, which appears many times in the New Testament, indicates the self-giving love of one who looks exclusively for the good of the other. The word eros, on the other hand, denotes the love of one who desires to possess what he or she lacks and yearns for union with the beloved." Now, God is perfect. How can God lack anything? What could God lack? It is the mystery of God who is Love itself that God created humanity for union with Himself. God loves us with an infinite love and desires only that we receive and return that love.
Pope Benedict goes on to point out that Old Testament passages in Hosea and Ezekiel and The Song of Songs "indicate that eros is part of God's very heart: The Almighty awaits the 'yes' of His creatures as a young bridegroom that of his bride." God's eros or passionate love of us is so strong that it leads to His agape, His self-sacrificing love. "On the cross, God's eros for us is made manifest."
Then he goes on to say: "Dear brothers and sisters, let us look at Christ pierced on the cross! He is the unsurpassing revelation of God's love, a love in which eros and agape, far from being opposed, enlighten each other. On the cross, it is God Himself who begs the love of His creature: He is thirsty for the love of every one of us. ... One could rightly say that the revelation of God's eros toward man is, in reality, the supreme expression of His agape. ... The response the Lord ardently desires of us is above all that we welcome His love and allow ourselves to be drawn to Him."
A simple way of seeing how the eros and agape of God is to think about our one English word "passion" which has two meanings. The Heart of Jesus is both passionate and wounded. The passion of Jesus for us led to His Passion.