The term “Incarnation” comes from a Latin word that means “in flesh.” It means that God took on human nature. Because it was God the Son, the Second Person of the Trinity, who became incarnate or in flesh, it is probably more correct and proper to say that it was the Logos or the Word that became flesh, rather than saying that God became a man, though both statements are actually true. The Incarnation means that suddenly there were two natures in one Person. The two natures were always distinct and never mixed within the one Person.
The most extended passage is John 1:1‑14. Notice that in the beginning the Word was with God (v. 1b), the Word was God (v. 1c) – God the Son – and the Word became flesh (v. 14). The Word that was in the beginning with God, that was God, at a certain point in human history took on flesh, became man, and that was the Incarnation.
Two key phrases concerning the Incarnation are found in Romans 1:3-4: according to the flesh (v. 3) and according to the spirit of holiness (v. 4). This is the Incarnation. He became man according to the flesh. It was accomplished by the power of the Holy Spirit; therefore, it was according to the Spirit as well.
In Phil 2:6-8 we see that “One” always existed in the form of God (v. 6); for all eternity past, He existed in the form of God, because He was the Second Person of the Trinity, God the Son. Secondly, He that existed in the form of God for all eternity, at some point in human history, was made into the likeness of men (v. 7). That is the statement of the Incarnation: He was made into the likeness of sinful men. The use of the term likeness does not mean He was not really a man. The term likeness emphasizes the similarity to sinful men in that, by mere observation, He did not look any different than any other human being. Except, in His case, He did not commit a single sin. He was an absolutely real human being, a real man, but not a sinful man. Thirdly, He was found in fashion as a man (v. 8).
Two other passages are worth mentioning here. In 1 Tim 3:16 Jesus was manifested in the flesh and in Heb 2:14 Jesus partook of flesh and blood, both references to the Incarnation.
 This post is a modified version of Dr. Arnold Fruchtenbaum’s original Messianic Bible Study. The full version may be obtained here.