Because of Jesus' humility and obedience, and in light of the fact that every knee should bow before Him, Christians must "work" out their salvation with fear and trembling! That is Paul's main point here. Now, don't misunderstand his usage of the word "work". Paul doesn't mean that there are some things we can do to earn or deserve our salvation from God. Such a notion would be contradictory to the New Testament elsewhere (e.g., Eph. 2:8,9). What Paul meant was that these Christians in Philippi needed to continue doing that which they had already begun (i.e., living a faithful life for the Lord)! The same is true for Jesus' disciples today. Once a person becomes a Christian by being baptized into Jesus, then they have begun to "work" out their salvation. This is something that must be continued "with fear and trembling"; that is, with all seriousness and reverence. To work out one's salvation as a Christian is to continue to live obediently to God while giving Him the respect and honor He deserves--whether anyone is watching us or not. One who only obeys God when others are watching him is not working out his salvation properly.
Philippians 2:13 begins with the word "for" which indicates that an explanation is about to be given for what had just been declared. Paul had been talking about obedience and work, and he here declares that God is the One who works in Christians. God works in His children both to "will" (i.e., desire) and to "do" (i.e., accomplish) His good pleasure. Paul is admonishing them to continue obeying God by realizing that in so doing they are allowing God to work in and through them, thereby accomplishing heaven's will.
If you're having difficulty understanding how God can work in and through us while we possess free will, please consider, for a moment, what the Bible teaches regarding faith and baptism. (1) Faith itself is a work of God (John 6:28,29). However, faith is something that each individual must determine for himself; that is, whether he will believe or reject what he has heard. The point is that when we believe (or develop faith) by hearing God's word (cf. Rom. 10:17), God is working in us (whether we realize it or not). (2) Baptism is also a work of God. Although baptism is something that a person chooses to submit to, it is still referred to as the working of God (Col. 2:12). God works in us when we believe, when we are baptized, and when we continue to do His will! How? He works in us and through us via the power of His inspired word. His word produces in us the desire to work which then enables us to actually accomplish what He wants done.
We will continue this study tomorrow.