What does it mean that Jesus became flesh

Lets understand what it does not mean first. It does not mean that his deity changed nature and became flesh. Nor does it mean that his flesh was made into deity.

Both the flesh and his deity are two different natures that dwelt in the same person.

We need to define what it means when it says he took on flesh. Jesus made the distinction John 3:6 "That which is born of the flesh is flesh, and that which is born of the Spirit is spirit.” Are two different properties, one is physical the other is immaterial.

The importance of this doctrine of human nature cannot be lessened or modified and neither can deity.

Romans 8:3 “sending His own Son in the likeness of sinful flesh”

In the likeness of sinful flesh, means he had a human body, the nature of man, but not sinful, he was a man without any of its sinful properties.

(Romans 8:3 [In the likeness of sinful flesh], [en (NT:1697) homoioomati (NT:3624) sarkos (NT:4508) hamartias (NT:263)]-literally, `in the likeness of the flesh of sin.' a very remarkable and pregnant expression. `It is not in the likeness of flesh'-for truly He "was made flesh" (John 11:14)-but `in the likeness of the flesh of sin;' in other words, He was made in the reality of our flesh but only in the likeness of its sinful condition. (See the excellent observations of DeWette.) [Similitudo-says Tertullian, quoted by Meyer-ad titulum peccati pertinebit non ad substantioe mendacium; referring to the Docetic heresy of our Lord's having assumed only an apparent Humanity.](from Jamieson, Fausset, and Brown Commentary)

Romans 8:3 In the likeness of sinful flesh en (NT:1697) homoioomati (NT:3624) sarkos (NT:4508) hamartias (NT:263). For "likeness" see Philippians 2:7, a real man, but more than man for God's "own Son." Two genitives "of flesh of sin" (marked by sin), that is the flesh of man is, but not the flesh of Jesus. (from Robertson's Word Pictures in the New Testament)

Romans 8:3since He was really and entirely human; but, "in the likeness of the flesh of sin:" really human, conformed in appearance to the flesh whose characteristic is sin, yet sinless. "Christ appeared in a body which was like that of other men in so as it consisted of flesh, and was unlike in so far as the flesh was not flesh of sin" (Dickson). (from Vincent's Word Studies of the New Testament)

Rom 1:3 “Concerning His Son Jesus Christ our Lord, who was born of the seed of David according to the flesh.” He could not be considered the son of David without being part of the lineage which would have to do with the blood line not just being in human form.

He was a descendant of David in his human nature, as a man. Of course, that he had another nature besides his humanity, while he was a man he was also something else; that there was a nature which was not descended from David, his deity from heaven which had no beginning. (Romans 9:5; Micah 5:2).

Becoming flesh is the means by which the invisible God became visible to man, not just as a manifestation but taking up a body that will forever continue. God communicated to man in ancient times by His word through the prophets (Heb.1:1) but now has communicated to us directly through His Son who became man.

John 1:14: “The word became flesh and dwelt among us and we beheld His glory, the glory as the only begotten of the Father.” The Word “became,” in Greek, ginomai, means a change of position, not a change of substance. Flesh in Greek is en sarke.  Here Jesus’ glory relates to that only of the Father. Implying that he who had pre-existence became united with the man. 

We need to be balanced in our understanding of just how man was to reflect his image. D.E. Trueblood said, “To say God is completely different from us is as absurd to say that he is completely like us.”

Speaking of Jesus in Phil.2:5: “Who being in the form of God did not consider it robbery to be equal with God.” V.7: “But made Himself of no reputation, and took upon Him the form of a servant, and was made in the likeness of men:”

     The form of God is Spirit that is His essence of being. We see that Christ has this same form. The Greek word for “form” is morphe, meaning that quality, the essential character that makes something what it is. Here Christ already existed in this nature and did not consider it to be robbery to be equal with another who is God. He did not have to covet or strive for His position; it was something He already possessed in eternity. Christ did not have to assert equality with God, but instead, emptied himself of what was rightfully his by becoming a man, a servant. This was a change of position, not a change in nature. He as God could not empty himself of His essential nature since unchangeableness is part of this. All His attributes are eternal, He could not eliminate any but He could put their independent used aside as He became a man and lived in submission.

Phil.2:7: “But made himself of no reputation taking the form of a bond servant, being made in the likeness of men.” This emptying was not a substance change of nature, but a putting aside of his position. It means while possessing all the nature and attributes of deity He did not use them for his own personal use but only for His Fathers will and pleasure. He did not do anything without first being instructed by the Father, perfect submission.

The phrase “the form of a bond servant” is identical in its content of the former “form,” “the form of God.” The later “form” being all that makes one a servant. He, as the Son, true deity, voluntarily laid aside using His divine attributes and privileges and entered the world of human existence taking on the role of a servant to humanity by adding a human nature to His deity.