Do everything without complaining or arguing,
(v14, NIV)
We are to look to the example of Jesus who was humbly obedient to the point of death. In our obedience to the Lord, we are not to complain or argue. An obedient person does not obey with complaining and arguing; they simply obey. Jesus did not complain or argue in his obedience. We are not to do either.
so that you may become blameless and pure, children of God without fault in a crooked and depraved generation, in which you shine like stars in the universe
(v15, NIV)
Why should we not complain or argue? This is so that we may become blameless and pure. The purpose is for our righteousness, so that we might be without spot or wrinkle. In the process of sanctification, we become more like Christ. As human beings, we are born into this world as dirty sinful creatures. However, we were washed and cleansed by the blood of Jesus Christ. Not everyone is saved, but those who are saved are washed white as snow. As we live on the earth, there are other humans among us. In comparison to them, we are like the stars. We shine bright amongst the vast night sky.
as you hold out the word of life—in order that I may boast on the day of Christ that I did not run or labor for nothing.
(v16, NIV)
We are being washed and we are being cleansed to be pure and spotless. We who are shining like the stars are holding out the word of life. This means that we are proclaiming the gospel to others. The gospel is that which gives life and this is the word that we hold out and tell others about. We do not just keep to ourselves, but gladly proclaim the word of life that graciously saved us.
In this obedience that leads to sanctification and the spreading of the gospel, Paul wishes to boast. Paul is partly to blame for their coming to know the Lord Jesus Christ. As followers of the Lord Jesus Christ, we obey him in his instructions to us. Paul was obedient in spreading the gospel to others and building up the church of believers. When you work hard at something and accomplish something, you can feel proud for your work. A painter may be proud of his painting and a carpenter may feel proud for something he built. In addition, people may feel proud for the work they did, like a firefighter putting out a fire. The work Paul did in the believers at the church in Philippi is work he can be proud of. He is encouraging them in their walk with Christ knowing and hoping that they continue till the end. If they prove to be true followers of the Lord Jesus Christ and continue in obedience to the Lord until the end, Paul can be proud for the work that he did. This doesn't mean that it was a wasted effort if Paul converted nobody to Christ. We do not convert people, it is God who does the converting.
What, after all, is Apollos? And what is Paul? Only servants, through whom you came to believe—as the Lord has assigned to each his task. I planted the seed, Apollos watered it, but God made it grow. So neither he who plants nor he who waters is anything, but only God, who makes things grow. The man who plants and the man who waters have one purpose, and each will be rewarded according to his own labor. For we are God's fellow workers; you are God's field, God's building.
(1 Corinthians 3:5-9, NIV)
As servants of the living God, we are simply gardeners. We may plant or we may water the plant, but we do not cause the growth. God is the one who causes the growth. In the same way, we may tell others about Jesus or we may help build up the body of Christ, but we do not cause their growth in the Lord. God causes their growth.
Paul's part in planting or watering is something he can still be proud of, even if he did not cause the growth. He can be proud that he took part in the growth of a true child of God. A plant that grows to be fruitful can be one that Paul is proud of. It's not like Paul watered something that simply withered away and died. That may be true for some of the plants he planted or watered, but he can be proud of the ones that flourished.