The concept of "emptying" was a raging controversy in the nineteenth century, and elements of it remain today. The Greek word used by Paul in the second chapter of Philippians, kenosis, is translated as "emptying" in most Bible versions. The question is, Of what did Jesus, in his human (incarnate) state, empty himself?
The popular view in certain circles in the nineteenth century was that at the time of the Incarnation, the eternal God, the second person of the Trinity, laid aside—emptied himself of—his divine attributes so that he could become a man. And in becoming a man in the very real sense, he stopped being God. And so there is the transformation from deity to humanity because he set aside his omniscience, his omnipotence, his self-existence, and all of those other attributes that are proper to the nature of God.
There was one orthodox theologian during the middle of that controversy who said somewhat caustically that the only emptying that theory proved was the emptying of the minds of theologians who would teach such a thing as God stopping for one second to be God. If God laid aside one of his attributes, the immutable undergoes a mutation; the infinite suddenly stops being infinite; it would be the end of the universe. God cannot stop being God and still be God. So we can't talk properly of God laying aside his deity to take humanity upon himself. That is why orthodox Christianity has always declared that Jesus was verus homus, verus Deus—truly man, truly God; fully man and fully God. His human nature was fully human, and his divine nature always and everywhere was fully divine.
Nevertheless, the apostle Paul does speak of Christ emptying himself of something. I think the context of Philippians 2 makes it very clear that what he emptied himself of was not his deity, not his divine attributes, but his prerogatives—his glory and his privileges. He willingly cloaked his glory under the veil of this human nature that he took upon himself. It's not that the divine nature stops being divine in order to become human. In the Transfiguration, for example (Matt. 17:1-13), we see the invisible divine nature break through and become visible, and Jesus is transfigured before the eyes of his disciples. But for the most part, Jesus concealed that glory. I think Paul is saying in Philippians 2 that we're to imitate a willingness to relinquish our own glory and our own privileges and prerogatives.