The above passages, though the Philippians were written to by Paul in this message above from the second chapter, in verse 12, he encouraged the believers there he deemed beloved, just as you have always obeyed (meaning obeying the commandments of Christ (love God first, and love others), not only in Pauls presence, but now even more in Pauls absence.
After Paul having addressed with them first time and had been with them, these believers of Philippi, even obeyed what Paul had brought forward to them. Even in Pauls absence these believers continued to obey. Paul mentions to them, continue to work out your salvation with fear and trembling.
There is something to think about here in verse 13, Paul mentioning to a group of believers, who were already obeying, to continue to work out their (individual) salvation with fear and trembling. This fear could be as scared, or in awe but also trembling. What could this mean? It seems to be a direct statement for individuals there to work out their own salvation with fear and trembling to continue in obedience towards Christ in faith towards God, and to allow God to work in them, (which he works with-in them by and through the Holy Spirit) and to act on behalf of His good purpose.
Working out ones own salvation is to continue to obey the commandments Christ had laid out having love for God first, and to love your neighbor as yourself. Mentioning that by doing this, they are allowing God to work in and through their life, which by and through the Holy Spirit, or the spirit of Christ - in faith you respond in the world, by and through the spirit on behalf of God's good purpose. Got all that?
Paul goes on to explain in verse 14, do everything without complaining or arguing. This right here is something very difficult for us to do sometimes as our flesh likes to complain and argue, even on any given subject issues, and problems that come up about in life, that one has experienced. However Paul is making it plain as day here, to do everything without complaining and arguing. Why? What is the purpose he is telling these people in Philippians to interact this way for? So that in verse 15 - they may be blameless and pure, children of God without fault in a corded and perverse generation (the current generation these people were living in was crooked and perverse according to Paul), thus he was encouraging them to do everything without complain or arguing - so that no one could say anything bad about them which made them blameless, and pure!
What an tall order to fulfill, to be seen as blames and pure, Children of God. Is this possible for us today? To some degree sure it is, to do everything without complaining or arguing, but is it easy? By far no, not without the strength of Christ, the Holy Spirit, and the Spirit of Christ to help us, asking the Father in heaven with prayer, however all of us have our shortcomings, Paul was very specific for them to be as shining lights in the world which could be you today.
Verse 16; to be lights in the world as they are hold on to the word of life in order that Paul may boast in the day of Christ that Paul did not run and Labor in vain. I wonder if this day is pertaining to the day that Christ would return, even though Paul would have been dead before He had come (though resurrected on that day that Jesus did come), either way it goes. Paul is encouraging people here to work out their own salvation with fear and trembling, to allow God to work in and through them, to do everything without complaint and arguing, so that they may be blameless and pure as Children of God, to be lights in the world as they live.
These same principles can apply to us spiritually today, when we do complain and argue that can quench the spirit if you are not having love for God first, and love for others. Working out your own salvation is a personal journey of course people come along the way, but you are responsible for your actions and what you do with your life with God either in your life by your faith, or God not in your life, with no faith at all. The biggest help is having the mind of Christ, and having Christ as our life by and through faith on the death, burial, and resurrection which is mainly common knowledge, living in faith trusting God, to help us and get us through this world by the spirit.
