Consider what that means: His heart, soul, mind, and will were only human - filled with the Holy Spirit, but human - like yours and mine. So when we see Jesus loving and expending Himself in the Gospels, those are human actions that we are witnessing! Oh, they are elevated by Grace and enflamed by the Holy Spirit to be sure, and there's no deformity or tainting from sin - but they're performed in His human nature.
Salvation is to be caught up into the HUMANITY of Jesus Christ - for our brokeness to find healing in His wholeness. The Holy Spirit is meant to flow through our souls, breaking forth in actions and words, just as they did in Jesus. In Jesus, through Baptism and the other Sacraments, our human souls "partake in the divine nature."
I was struck this past weekend by the beauty of devotion to Jesus' Sacred Heart. It is His human heart that we are reverencing. His human heart - the perfect conduit of the fiery, Divine Love. And we are called to share in, to participate in, His Sacred Heart! This is what we see in the saints - Maximilian Kolbe giving his life in exchange for another prisoner's, Mother Teresa working away in the slums of Calcutta, and Gianna Molla's love for her patients and children. Those words Jesus spoke at the Last Supper are just waiting to be lived out, "Anyone who has faith in me will do what I have been doing. He will do even greater things than these, because I am going to the Father" (John 14:12).