Excerpt of a letter by St. Athanasius from today's Office of Readings (as found on the Universalis website).
By taking our nature and offering it in sacrifice, the Word was to destroy it completely and then invest it with his own nature, and so prompt the Apostle to say: This corruptible body must put on incorruption; this mortal body must put on immortality.
In addition to the above quote, St. Athanasius also wrote, “For the Son of God became man so that we might become God.” (On the Incarnation) And this last quote is found in the Catechism of the Catholic Church along with many other similar quotes of other great saints throughout the ages. This is all in reference to the Church's belief in the divinization of man, which happens as a result of Incarnation of God. It is not my intent to pontificate about this lofty subject. Instead I am going to let von Hildebrand explain it.
Christ, the Messiah, is not merely the Redeemer who breaks apart the bond and cleanses us from sin. He is also the Dispenser of a new divine life which shall wholly transform us and turn us into new men: 'Put off the old man who is corrupted according to the desire of error, and be renewed in the spirit of your mind; and put on the new man, who according to God is created in justice and holiness of truth.' Though we receive this new life in Baptism as a free gift of God, it may not flourish unless we cooperate. 'Purge out the old leaven, that you may be a new paste,' says St. Paul.
A strong desire must fill us to become different beings, to mortify our old selves and rearise as new men in Christ. This desire, this readiness to decrease so that 'He may grow in us,' is the first elementary precondition for the transformation in Christ. It is the primal gesture by which man reacts to the light of Christ that has reached his eyes: the original gesture directed to God. It is, in other words, the adequate consequence of our consciousness of being in need of redemption on the one hand, and our comprehension of being called by Christ on the other. Our surrender to Christ implies a readiness to let Him fully transform us, without setting any limit to the modification of our nature under His influence.
From Transformation in Christ