The historic, orthodox, patristic sense of passages, in particular ones like Psalm 82:6 and 2 Peter 1:4, is what is known as the Christian doctrine of Theosis. We see this in grand statements such as by St. Irenaeus, "The Lord became what we are that we might become what He is", or St. Athanasius "[God] became man so that man might become God".
Those are certainly fascinating statements and by themselves could sound very odd, especially to modern Western Christian ears not particularly well accustomed to such language. But it's language that has long been resonant within Christianity, both East and West, right up until the present. In C.S. Lewis' famous Mere Christianity he writes,
The command Be ye perfect is not idealistic gas. Nor is it a command to do the impossible. He is going to make us into creatures that can obey that command. He said (in the Bible) that we were gods and He is going to make good His words. If we let Him for we can prevent Him, if we choose He will make the feeblest and filthiest of us into a god or goddess, dazzling, radiant, immortal creature, pulsating all through with such energy and joy and wisdom and love as we cannot now imagine, a bright stainless mirror which reflects back to God perfectly (though, of course, on a smaller scale) His own boundless power and delight and goodness. The process will be long and in parts very painful; but that is what we are in for. Nothing less. He meant what He said.
In the historic Christian meaning Theosis is not like the Platonic return to origin--the soul of man having descended down through emanations into the lowlier world of matter, only to be taken back up again into the infinite world of the Good. It is instead a teleological work by which God having created human beings--flesh and blood creatures that we are--in the Divine Image means He is going to make good on that. And of course to be created in the Image of God is to mean, very simply, that the human creature is God's image-bearer, a creature that reflects the Divine goodness to the rest of creation and therefore brings honor and glory to God. The Divine Image is not ontological, but functional, it's what man was created for. Sin, of course, has damaged the image; but again God is going to make good on what He's said and done. In Christ, therefore, God has condescended to meet man right here in his sin and death, and by death and resurrection, overcome these and put them beneath His feet. Thus as risen from the dead He has taken humanity in Himself, by His own body, and raised it from death to life. And thereby having assumed our humanity, calls us to a life together in Him and with Him which will be accomplished on the future coming day when God sets the world and all things to rights.
Even as God having come and met us in our humanity has called us, in Himself, to meet God in Him, and thus to know God by Him, and to share in God with Him. And thus to be in Christ, and ultimately that means that we will be raised up, bodily, from the grave to eternal life right here on God's good, renewed, green earth is to share in the sort of life that Christ has. Which, as eternal Son of the Father, is the very life of God.
And to therefore share in God's own Divine Life, as grace in Jesus Christ by His death and resurrection, and the reality of that future life and world--that means very much, "ye are gods". To be a thing that really does reflect that love and goodness and light and glory of the good Creator God.
Not to be subsumed away from our individual and creaturely identities into a great amorphous mass of impersonal divinity; but to be brought into that kind of communion and fellowship with God that whereby we are, fundamentally, transformed by God, and are as God intended. Truly, really human.
That's actually kind of the upside-down counter intuitive nature of the thing. The irony is that in man aspiring to be divine in a sense lost their humanity, and it is that God has taken upon Himself our humanity and restored it, that in God we again recover and become really and actually human.
Roman Catholic theologian Herbert McCabe puts it this way:
"Jesus is God's Word, God's idea of God, how God understands himself. He is how-God-understands-himself become a part of our human history, become human, become the first really thoroughly human part of our history - and therefore, of course, the one hated, despised, and destroyed by the rest of us, who wouldn't mind being divine but are very frightened of being human."
In that sense Theosis, the divinization of man is fundamentally the re-humanization of man in God, in the God who became man.
-CryptoLutheran