I heard John use the term "hypostatic union."
What does that mean and where did it come from?

The theological term "hypostatic union" has its origins in the Council of Chalcedon and emphasizes that Jesus Christ was fully God and fully man at the same time. It is used to affirm the union of Jesus' divine and human natures in one person--that Jesus Christ is perfectly God and perfectly man. Or, as theologians say, He is consubstantial with God as to His deity and with mankind as to His humanity.

Soon after the establishment of the church, doctrinal errors arose concerning the person of Jesus Christ. In October of A.D. 451, a large church council convened in the city of Chalcedon near Constantinople. After much discussion, the Council issued a statement to correct the errors and to establish an accurate theological statement concerning the person and nature of Christ. The fruit of their labor is perhaps the most significant Christological statement in the history of the church:

We, then, following the holy Fathers, all with one consent, confess one and the same Son, our Lord Jesus Christ, the same perfect in Godhead and also perfect in manhood; truly God and truly man, of a reasonable [rational] soul and body; consubstantial [coessential, of the same substance] with the Father according to the Godhead, and consubstantial with us according to the Manhood; in all things like unto us, without sin; begotten before all ages of the Father according to the Godhead, and in these latter days, for us and for our salvation, born of the Virgin Mary, the God-bearer, according to the Manhood; one and the same Christ, Son, Lord, Only-begotten, to be acknowledged in two natures, inconfusedly, unchangeable, indivisibly, inseparably; the distinction of natures being by no means taken away by the union, but rather the property of each nature being preserved, and concurring in one Person and one Subsistence, not parted or divided into two persons, but one and the same Son, and only begotten, God, the Word, the Lord Jesus Christ, as the prophets from the beginning [have declared] concerning Him, and the Lord Jesus Christ Himself has taught us, and the Creed of the holy Fathers has been handed down to us.

So what errors did the Council of Chalcedon correct?

In order to correct the view of Apollinarius, who believed Christ did not have a human mind or soul, the Council wrote that Jesus was "truly man, of a reasonable [rational] soul and body ... consubstantial [coessential, of the same substance] with us according to the Manhood; in all things like unto us."

To correct the teachings of Nestorianism, that Christ was two different persons united in one body, the Council wrote that He was "indivisibly, inseparably ... concurring in one Person and one Subsistence, not parted or divided into two persons."

And finally, in rejecting the errors of Monophysitism, which taught Christ had but one nature and that His union with the Divine nature obliterated His human nature, the council wrote that Christ was "to be acknowledged in two natures, inconfusedly, unchangeably ... the distinction of natures being by no means taken away by the union, but rather the property of each nature being preserved."

For more information about the Person and Work of Jesus Christ, consider these resources:

• Christ Humbled, Christ Exalted
  -- four-part audio series from Philippians 2:5-11
• The Superiority of Christ
  -- seven part audio series from Hebrews 1--2