"The term hypostatic union is much easier than it sounds, but the concept is as profound as anything in the universe—the personal union of the eternal Son of God with our humanity.
The English adjective hypostatic comes from the Greek word hupostasis. The word only appears four times in the New Testament—maybe most memorably in Hebrews 1:3, where Jesus is said to be “the radiance of the glory of God and the exact imprint of his nature.” Here the author of Hebrews uses the word in reference to the oneness of God. Both the Father and the Son are of the same “nature.” Jesus is “the exact imprint of his nature.”.........So “hypostatic union” may sound fancy in English, but it’s a pretty simple term. Hypostatic means personal. The hypostatic union is the personal joining of Jesus’ two natures in one person.
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."