In the first part of this passage, Paul encourages the followers in Philippi to "empty" themselves in the same way that Jesus did. This idea is derived from the image of believers completely emptying themselves of any ideas or thoughts of their own so as to be completely open and receptive to the grace and leading of God.
Paul is saying that Jesus "who, though he was in the form of God, did not count equality with God a thing to be grasped" (Phil. 2:6) didn't need to do this since he was already united with God in form and thought. Since Jesus had taken human form, however, He "emptied himself" (Phil. 2:7a) and "became obedient unto death, even death on a cross." (Phil. 2:8b) Paul is illustrating the way in which the Philippians should be striving to live, giving up their human natures and opening themselves to God's leading.
Verses 9-11 are a proclamation of praise, affirming the high praise God has given Jesus because he obeyed God's will while he was living as a human being. Now, Jesus has been "highly exalted" (Phil. 2:9) and given the greatest name and position of all. In response to the glorious honor and power and forgiveness encompassed by the name of Jesus,
every knee should bow, in heaven and on earth and under the earth, and every tongue confess that Jesus Christ is Lord, to the glory of God the Father. (Phil. 2:10-11)
Paul calls on all living things on earth, below the surface, and in the sky and heavens, to join in affirming the Lordship of Jesus and the great glory of God.