“Hypostatic” is a strange word for most of us, but it really is quite simple. It comes from the Greek word “hupostasis”  and means “personal.”  The hypostatic union refers to the personal union of the two natures of Jesus Christ. It is used 4 times in the Bible. One example is Hebrews 1:3 where Jesus is called “the radiance of the glory of God and the exact imprint of his nature.”

Jesus has two complete natures—one fully human and one fully divine. What the doctrine of the hypostatic union teaches is that these two natures are united in one person in the God-man. Jesus is not two persons. He is one person. The hypostatic union is the joining of the divine and the human in the one person of Jesus.
David Mathis

This was why the Jews were seeking all the more to kill him, because not only was he breaking the Sabbath, but he was even calling God his own Father, making himself equal with God.  
John 5:18

It is this amazing union of God and Man that we celebrate this Christmas season. That God would take on flesh and become, in all aspects, human, and yet lose none of his divinity is a wonder and an amazing grace.

Jesus had a reason for becoming man. It was Christ who would undo the curse of death, repair hearts mangled by sin, and appease the wrath of an infinity Holy Father. Only a man could die for the sins of men and only God could offer a sacrifice valuable enough to appease the wrath of an infinitely holy God. Nothing less than the God-man could bring about salvation.

Jesus was God and man in one person, that God and man might be happy together again.
George Whitfield

It’s mind-boggling to think that Jesus was somewhat finite and totally infinite at the same time, that he was all-knowing and yet chose to learn, that he was all-powerful and yet allowed himself to be beaten and killed. It does not fully compute in my brain how Jesus could die and yet God cannot.

It is by far the most amazing miracle in the whole Bible-far more amazing than the resurrection and more amazing than the creation of the universe. The fact that the infinite, omnipotent, eternal Son of God could become man and join Himself to a human nature forever, so that infinite God became one person with infinite man, will remain for eternity the most profound miracle and the most profound mystery in all the universe.
Wayne Grudem

Even more amazing is that Jesus did all of this for me, for you! The hypostatic union of Jesus continues even today. He still has a body that will forever remind all of his great love for his people.

Touching His human nature, Jesus is no longer present with us. Touching his Divine nature, He is never absent from us.
R.C. Sproul