What are Christian theologeans referring to when they talk about "God's glory"? What is God's "glory" in Christian theology? (If it differs based on which branch of the church is using the term, give me a brief summary of the Catholic, Orthodox, and Protestant views.)

Are we talking about God's "glowing radiance" when we speak of His glory, or does it have more to do with other peoples' "recognition and honor" of Him?
The Hebrew word for Glory -  'Kabod'   means weightiness. In the Old Testament this was the Shekinah Glory that filled the temple visibly
Exo_33:22  When my glory passes by, I will put you in a cleft in the rock and will cover you with my hand while I pass by.
Deu_5:24  You said, "The LORD our God has shown us his great glory and we have heard him speak from the middle of the fire. It is now clear to us that God can speak to human beings and they can keep on living.

In the New Testament, after the Messiah's work of deliverance was complete, we see God's glory as a spiritual essence until the Second coming of Christ:
Rom_3:7  For if by my lie the truth of God enhances his glory, why am I still actually being judged as a sinner? Here, humans give glory (or all due respect and credit) to God.

Mat_16:27  For the Son of Man will come with his angels in the glory of his Father, and then he will reward each person according to what he has done. Here, Messiah comes again as God who is full  of the Father's Glory.

So, there is consistency in the use of Glory in scripoture wherein it describes God's omniscience and omnipotence, and is manifested is His radiance.