K. Scott Oliphint writes,
What then does Paul mean when he says that this preincarnate Son, who was in the form of God but who took on the form of a servant “made himself nothing”?. . .
We are, says Paul, to incubate within ourselves the same mind-set that Christ himself had when he chose to come down to us. More specifically, we are told, “do nothing from rivalry or conceit, but in humility count others more significant than yourselves” (Philippians 2:3). We are not, then, to hold on to whatever status or position we think we might own, but rather to consider that the position or status of others is more significant.
In this light and because of this context, it becomes clearer to us what Paul is saying about our Savior. In his decision to take on the likeness of humanity, he did not simply look to his own position or status, nor did he count that position or status something that he should, in every way, protect and maintain. Rather he considered the position of those who are lower, who could not reach up to his position, and he determined to stoop down to their level. . . .
It is not as though Christ emptied himself of something; that is not what Paul actually says. His actual point is that Christ emptied himself by becoming something that he was not previously, something that, by definition, required humility and ultimately humiliation (Philippians 2:8). For Christ to make himself nothing, says Paul, was for him to humble himself, and he humbles himself by being born in the likeness of men and by becoming obedient to the point of death. So, as Paul describes it in this passage, the self-emptying is, in point of fact, a self-adding.
God With Us: Divine Condescension and the Attributes of God, (Wheaton: Crossway, 2012), 118, paragraphing added.