Taking up St. John’s expression, “The Word became flesh”,The Church calls “Incarnation” the fact that the Son of God assumed a human nature in order to accomplish our salvation in it. In a hymn cited by St. Paul, the Church sings the mystery of the Incarnation:
Have this mind among yourselves, which is yours in Christ Jesus, who, though he was in the form of God, did not count equality with God a thing to be grasped, but emptied himself, taking the form of a servant, being born in the likeness of men. and being found in human form he humbled himself and became obedient unto death, even death on a cross.
The Letter to the Hebrews refers to the same mystery:
Consequently, when Christ came into the world, he said, “Sacrifices and offerings you have not desired, but a body have you prepared for me; in burnt offerings and sin offerings you have taken no pleasure. Then I said, Lo, I have come to do your will, O God.”
Belief in the true Incarnation of the Son of God is the distinctive sign of Christian faith: “By this you know the Spirit of God: every spirit which confesses that Jesus Christ has come in the flesh is of God.”Such is the joyous conviction of the Church from her beginning whenever she sings “the mystery of our religion”: “He was manifested in the flesh.”
From the Catechism of the Catholic Church 461-463