St. Gregory Palamas starts to get technical in the second paragraph of his Homily Fifty-Eight on the Saving Nativity According to the Flesh of Our Lord and God and Savior. Two words that jump out, because of their technicality are “theandric hypostasis.”
Theandric is a compound Greek word which combines θεός (God) and άνδρaς (man). Thus, Palamas is referring to Christ as the God-man and the fact that He is both God and man.
Hypostasis, from the Greek ὑπόστᾰσις, is a much more difficult word. Although it can have several meanings (including support, ambush, deposit and sediment) it is rarely used except as a technical medical/philosophical word meaning “everything that settles” which becomes “existence” or “reality.” The Latin translation becomes the root of “substance” in English. It is also the root of the modern Greek verb υπάρχω, which means “to exist.”
Some Stoic philosophers used hypostasis in contrast with οὐσία (meaning “essence”) where οὐσία is the unformed pre-existant essence and ὑπόστᾰσις is that which attains reality.
The word is rarely used in Scripture and is found in the NT only five times. Twice it is used to mean “support.” The other three are all found in Hebrews, the most useful being found in 1:3 where ὑπόστᾰσις is translated and understood as “being”:
He is the reflection of God’s glory and bears the impress of God’s own being.
It is from this usage that the Church forms the dogmatic statement about the Trinity: God is one in essence (οὐσία) and three in hypostases (ὑπόστᾰσις). In a similar way that the Stoics used these two words to describe the characteristics of matter, the Church Fathers use οὐσία and ὑπόστᾰσις in a way to describe two different characteristics of God — His essence and His being. This language is imperfect because God cannot be contained by language; however it is useful in that it helps clarify what God has revealed to us about Himself.
Generally, when we translate this dogmatic formula into English, we translate ὑπόστᾰσις as “person” — three persons in one essence. Again, this is imperfect but useful, especially when it comes to the salvific nature of the Nativity of Christ.
Since we are made in the image and likeness of God, we share in His Trinitarian way of being. We are all individual persons (ὑπόστᾰσις) and we all share our humanity (οὐσία). Thus, when Christ unites Himself to our humanity (οὐσία) He saves all of us. Yet, we must choose to participate in this salvation as individual persons (ὑπόστᾰσις).
Thus, when St. Gregory Palamas uses the technical term “theandric hypostasis” he is referring to the being of Christ — He has united His person to our humanity to become the God-Man and our means of salvation and union with God.