Dictionary.com

noun
1. an incarnate being or form.
2. a living being embodying a deity or spirit.
3. assumption of human form or nature
4. the Incarnation, (sometimes lowercase) Theology. the doctrine that the second person of the Trinity assumed human form in the person of Jesus Christ and is completely both God and man.
5. a person or thing regarded as embodying or exhibiting some quality, idea, or the like: The leading dancer is the incarnation of grace.
6. the act of incarnating.
7. state of being incarnated.

Etymonline.com

c. 1300, “embodiment of God in the person of Christ,” from Old French incarnacion “the Incarnation” (12c.), from Late Latin incarnationem (nominative incarnatio), “act of being made flesh” (used by Church writers especially in reference to God in Christ; source also of Spanish encarnacion, Italian incarnazione), noun of action from past participle stem of Late Latin incarnari “be made flesh,” from in- “in” (from PIE root *en “in”) + caro (genitive carnis) “flesh” (originally “a piece of flesh,” from PIE root *sker- (1) “to cut”). Glossed in Old English as inflæscnes, inlichomung. As “person or thing that is the embodiment” (of some quality, deity, etc.) from 1742.

Discussion/Explanation

There are many myths of various beings taking a human form in history. In the case of Christianity, Jesus Christ was God incarnate in flesh even to be the point of being born into the world as any other human being.

Even to this day, the Incarnation of Jesus Christ still possesses mystery but there are many things that we do know.

1. God became incarnate as Son of God and Son of Man in Jesus Christ. He is God and man at the same time. This is important as it allows him to fulfill the role of being the last Adam and pay the price for sin brought into the world by the first Adam (the Adam of Genesis).
2. Despite being incarnate, Jesus is still part of the triune nature of God. God is multi-dimensional and is not bound by the same constraints as you are I. He is one.
   1. God the Father has no physical form and neither does the Holy Spirit.
      1. You will often see dove imagery for the Holy Spirit despite the Scriptures never describing the Holy Spirit to be a dove but was compared to a dove in Luke 3:22.
3. The Son did not give up His deity to become man though he does seem to restrain it.
4. The terms we use: Father, Son, Holy Spirit are very mortal terms used to describe this triune nature that is inherently beyond our full understanding (at least not in this lifetime and probably not even in the next after the end of all things).

There is much to be studied and discussed on this topic. But, suffice to say that the word “incarnation” in Christianity is a term brought up in reference to Christ’s being God as human.

A great work to read because of its historical significance to the doctrinal understanding of the incarnation of Christ would be On the Incarnation by Athanasius. The following link takes you to a pdf file of the work. (it’s free)

http://www.onthewing.org/user/Athanasius%20-%20On%20the%20Incarnation.pdf