In his book Dying to Preach, Steven Smith reflects on the meaning of Philippians 2:6 ("[Christ], being in very nature God, did not consider equality with God something to be grasped"):

While Christ took on the form of a human, he set aside his rights as God. In other words, all of Christ's time on earth he was always Godlike. When he was tried in Samaria, he was all-powerful; when he was asking questions in the temple, he was all-knowing; and when he was present in a particular place, he was omnipresent. It is simply that he made a choice not to take hold of what was always, and always will be, his—namely, his God-like properties.

Imagine that you are visiting a hospital. You cannot find a parking place close to the hospital, so you park way in the back, and now you are lost. You stop another driver in the lot to ask directions, and he kindly says that he will just park beside you and walk with you to where you need to be in the hospital. Now suppose that as you get to the front of the hospital, you find out that this man is actually the chief surgeon of the hospital, and as you near the door, he adds, "Oh, yes, and this is my parking place." He had a superior advantage because of his status. However, in deference to your needs, he did not take his rightful parking spot but walked with you the whole way. So here is the question: As he was walking with you, did he stop being a doctor? No. Did he have a parking place? Yes. He had all of these things and at any time could have laid hold of those things and used them, but for your sake he just chose not to in that particular moment.

As thin as that metaphor is, [it illustrates] that Christ's walking among human beings did not mean he was not God. Then why did he not reverse his tiredness or overcome all his physical limitations? It is because if he were to override his humanity, he would not have been fully in the form of a man and therefore could not fully empathize with our weakness or save us by his perfect life. The Incarnation was not just an event at Bethlehem. The Incarnation was the moment-by-moment choice of Christ to lay down his privileges, his rights as God, and to acquiesce to ungrateful sinners every second in order to effect our salvation.