The Apostle Paul explains it quite nicely at Philippians 2:3-8. Vs3, "Do nothing from selfishness or empty conceit, but with humility of mind let each of your regard one another as more important than himself; vs4, do not merely look out for your own personal interests, but also for the interest of others." This is not hard to understand because true love puts others first.
Vs5, Have this attitude in yourselves which was also in Christ Jesus." So what kind of an attitude and love did Jesus have? Vs6, who, although (although means in spite of the fact) He/Jesus existed in the form of God, did not regard equality with God a thing to be grasped."
vs7, but emptied Himself, (how?) by taking the form of a bond-servant, and being made in the likeness of men. vs8, And being found in appearance as a man, He humbled Himself by becoming obedient to the point of death, even death on a cross."
So what Jesus Christ did was go from one form as God and took on another form of a bond-servant/man. Instead of clinging to what was rightfully His before He became a man He forewent the prerogatives of His deity. That's what it means when it says, "He emptied Himself." John 17:5 states,
And now glorify Thou Me TOGETHER with Thyself, Father, with the glory I HAD WITH THEE BEFORE THE WORLD WAS."
Or to put this another way. Jesus the Son of God voluntarily submitted Himself to His Father. The Son was inferior to His Father in position only, but equal in nature. The President is superior in position because he is the President. He is not better than you in nature because he has the same human nature as we do.
Notice Hebrews 10:19-20. "Since therefore, brethren, we have confidence to enter the holy place by the blood of Jesus, vs20, by a new and living way which He inaugurated for us through the VEIL, that is His flesh."
Neither Christ's divinity, nor His Divine attributes, nor the use of those attributes, nor His glory, was in any way "emptied." Rather, these were concealed under a veil of flesh. Let me illustrate by saying that Howard Hughes was a billionaire and later in life he chose to live and look like a bum. His millions were veiled and if he wanted, he could have accessed his money at any time.
In short, Jesus emptied Himself or veiled Himself of the expression of deity, not the possession of deity. He did this when He became flesh.
The following is what Greek Scholar A.T.Robertson says.
Being (υπαρχων — huparchōn). Rather, “existing,” present active participle of υπαρχω — huparchō In the form of God (εν μορπηι τεου — en morphēi theou). Μορπη — Morphē means the essential attributes as shown in the form. In his preincarnate state Christ possessed the attributes of God and so appeared to those in heaven who saw him. Here is a clear statement by Paul of the deity of Christ. A prize (αρπαγμον — harpagmon). Predicate accusative with ηγησατο — hēgēsato Originally words in μος — ̇mos signified the act, not the result (μα — ̇ma). The few examples of αρπαγμος — harpagmos (Plutarch, etc.) allow it to be understood as equivalent to αρπαγμα — harpagma like βαπτισμος — baptismos and βαπτισμα — baptisma That is to say Paul means a prize to be held on to rather than something to be won (“robbery”). To be on an equality with God (το ειναι ισα τεοι — to einai isa theoi). Accusative articular infinitive object of ηγησατο — hēgēsato “the being equal with God” (associative instrumental case τεωι — theōi after ισα — isa). Ισα — Isa is adverbial use of neuter plural with ειναι — einai as in Revelation 21:16. Emptied himself (εαυτον εκενωσε — heauton ekenōse). First aorist active indicative of κενοω — kenoō old verb from κενος — kenos empty. Of what did Christ empty himself? Not of his divine nature. That was impossible. He continued to be the Son of God. There has arisen a great controversy on this word, a Κενοσις — Kenosis doctrine. Undoubtedly Christ gave up his environment of glory. He took upon himself limitations of place (space) and of knowledge and of power, though still on earth retaining more of these than any mere man. It is here that men should show restraint and modesty, though it is hard to believe that Jesus limited himself by error of knowledge and certainly not by error of conduct. He was without sin, though tempted as we are. “He stripped himself of the insignia of majesty” (Lightfoot).