The Incarnation is the claim that the eternal Son of God, without ceasing to be God, took to himself a complete human nature and lived as a specific first-century Jew. The technical name for the result is the hypostatic union: two natures, divine and human, united in one person. Of all Christian doctrines it is the one defined with the most precision, because the question of how the two natures relate turned out to be church-dividing.
The scriptural anchor is the prologue of John's Gospel, "the Word became flesh and dwelt among us" (John 1:14), read together with the hymn of Philippians 2, in which the one who was "in the form of God" empties himself and takes "the form of a servant." From these the tradition drew two non-negotiables it refused to soften: that the one who became incarnate was truly God, and that what he assumed was a real and whole humanity, body and rational soul. Everything defined later was an attempt to hold both at once without letting either collapse into the other.