The Incarnation is Jesus. The Incarnation emphasizes that Jesus is fully God and fully human. To explain this is to talk about Jesus but it is better to actually get to know Jesus. So we will first talk about that.
Gives: “For God so loved the world that He gave his only Son, that whoever believes in him should not perish but have eternal life.” (Jn 3:16)
This is the classic quote used to express God’s love for humanity. It connects the Trinity (God the Father giving God the Son) with the Incarnation (the giving of the Son) and the reason, to save humanity through faith.
Save humanity: “The Word became flesh for us in order to save us by reconciling us with God” (CCC 456)
The classic quote used to express the Incarnation is from John’s gospel, “The Word became flesh” (Jn 1:14). Jesus who is the Word of God assumed human nature (became flesh). It gives the reason for the Incarnation, ie redemption.
There are two aspects to the Incarnation, one identifies the action of God becoming man (first sentence) and the second is the reality of Jesus being God and man (second sentence). The Incarnation refers to both facts. The reason for the Incarnation is to save humanity which is expressed in the first sentence. It is important to realize that God the Son has always been the Son and is eternally the Son. Jesus as a human being who is God only came into existence when his humanity was united to his divinity. But we generally talk of Jesus always existing since He has always existed as a divine person. Just as the Son is eternally begotten of the Father, so the Father gives Jesus to humanity to save humanity, love humanity and share his divine nature with humanity.
Love: “The Word became flesh so that thus we might know God's love”(CCC 458)
How do we know God loves us? Jesus reveals God’s love to us, through what He has said and done, eg forgives us, heals us, teaches us the truth, and ultimately dies for us.
Divine: “The Word became flesh to make us "partakers of the divine nature"” (CCC 460, see DV 2)
Salvation can be seen from three aspects, forgiveness of sins, friendship with Jesus and sharing in the divine nature. In giving ourselves to God, we begin to participate in Trinitarian life, which means we start to share in the divine nature itself. The more we share our life with God (including our sin) the more God will share his divine life with us. The best part is friendship with Jesus. That Jesus personally guides us and helps us in life.
The Incarnation is Jesus being true God and true man like humans in all things but sinless. Not part God, part man, nor an assumed humanity.
Incarnation: “the Church calls "Incarnation" the fact that the Son of God assumed a human nature in order to accomplish our salvation in it.” (CCC 461)
True: “Jesus Christ is true God and true man.: (CCC 464)
Sinless: “like to us in all things except sin.” (GS 22)
Jesus never sinned. His every action was an action of love.
Not part: “the Incarnation …does not mean that Jesus Christ is part God and part man, nor does it imply that He is the result of a confused mixture of the divine and the human.” (CCC 464)
There are various ways people understood Jesus in the early Church. A lot of this was worked out at the early ecumenical councils. Some examples of these errors are that Jesus was part God and part man, but the truth is that Jesus is fully God and fully man.
Assumed: "human nature was assumed, not absorbed" (GS 22)
The difference between assumed and absorbed is that assumed maintains his personal nature, while absorbed would mean his humanity would be lost within the Trinity in some kind of state of common unity which would be impersonal.