To be empty is to be without something, and that's just the word Paul uses to describe what Jesus did when he divested himself of his godly form in order to become human. He emptied himself into human form. His very presence among us was the ultimate display of humility.
This understanding that God gave up all of His majesty, splendor, and, well, his godliness, in order to be human and dwell among us is quite amazing. It is also a pattern for our lives as Christians - that we should divest ourselves of ego as much as possible in order to become God's instruments in this life.
Lent's call to repentance is also a call to humility. To confess our sin and frailties is to recognize our inability to control our habits, ourselves, our lives. It is a commendation of God's supreme ability to better guide us in the living of our lives; it is an emptying of self in honor of God's will. Indeed, it is an imitation of Jesus.
Philippians 2. 5-11
2:5 Let the same mind be in you that was in Christ Jesus,
2:6 who, though he was in the form of God, did not regard equality with God as something to be exploited,
2:7 but emptied himself, taking the form of a slave, being born in human likeness. And being found in human form,
2:8 he humbled himself and became obedient to the point of death-- even death on a cross.
2:9 Therefore God also highly exalted him and gave him the name that is above every name,
2:10 so that at the name of Jesus every knee should bend, in heaven and on earth and under the earth,
2:11 and every tongue should confess that Jesus Christ is Lord, to the glory of God the Father.