Augustine on what Christ became

[Christmas] It is called the Lord’s birthday when the wisdom of God presented itself to us as an infant, and the Word of God without words uttered the flesh as its voice. Let us joyfully celebrate the coming of our salvation and redemption.

… For whose benefit did such sublimity come in such humility? Certainly for not of his own; but, if we are believers, totally for ours. Wake up, mankind, for your God became man!

… Let us celebrate the festal day on which the great and timeless One came from the great and timeless day to this brief span of our day. He has become for us ‘justice, and sanctification, and redemption;’ (1 Cor. 1.30, 31)

…. Hence, when the Lord whose birthday we are celebrating today was born of the Virgin, the announcement of the angelic choir was made in the words: 'Glory to God in the highest, and on earth peace among men of good will.' (Luke 2.14) How can peace exist on earth unless it be because 'truth is sprung out of the earth,' (Psalm 81.11) that is, because Christ has been born in the flesh? Moreover, 'He Himself is our peace, he it is who has made both one' (Eph. 2.14) so that we might become men of good will, bound together by the pleasing fetters of unity.

… Let us then rejoice in this grace, so that our glorying may bear witness to our good conscience by which we glory, not in ourselves, but in the Lord. That is why Scripture says: He is my glory, the one who lifts up my head (Psalm 3.4). For what greater grace could God have made to dawn on us than to make his only Son become the son of man, so that a son of man might in his turn become a son of God? Ask if this were merited; ask for its reason, for its justification, and see whether you will find any other answer but sheer grace.

Augustine, Sermon 185

Augustine on the Incarnation

But "the light shines in darkness, and the darkness comprehended it not." Now the "darkness" is the foolish minds of men, made blind by vicious desires and unbelief. And that the Word, by whom all things were made, might care for these and heal them, "The Word was made flesh, and dwelt among us." For our enlightening is the partaking of the Word, namely, of that life which is the light of men. But for this partaking we were utterly unfit, and fell short of it, on account of the uncleanness of sins. Therefore we were to be cleansed. And further, the one cleansing of the unrighteous and of the proud is the blood of the Righteous One, and the humbling of God Himself; that we might be cleansed through Him, made as He was what we are by nature, and what we are not by sin, that we might contemplate God, which by nature we are not. For by nature we are not God: by nature we are men, by sin we are not righteous. Wherefore God, made a righteous man, interceded with God for man the sinner. For the sinner is not congruous to the righteous, but man is congruous to man. By joining therefore to us the likeness of His humanity, He took away the unlikeness of our unrighteousness; and by being made partaker of our mortality, He made us partakers of His divinity. For the death of the sinner springing from the necessity of comdemnation is deservedly abolished by the death of the Righteous One springing from the free choice of His compassion, while His single [death and resurrection] answers to our double [death and resurrection]. De Trinitate 4.2.4