Paul wanted to encourage the Philippian believers, but what did he want to encourage them in? He wanted to encourage them in their faith. We all have had times that our faith was challenged, questioned, and shaken. Paul knew this and saw an opportunity to encourage others in their faith in our Lord Jesus Christ.
Jude 1:20 ESV But you, beloved, building yourselves up in your most holy faith and praying in the Holy Spirit,
Paul was in prison in Rome, which is enough to cause a person to be in great worry and anguish if he did not trust in the Lord. Paul knew also that he was facing execution for his preaching the gospel. He wanted to ensure the Philippian church that he was in peace and rejoicing in his faith in the Lord Jesus Christ.
Paul was content knowing that the truth of the gospel was going out.
Philippians 1:12-18 ESV (12) I want you to know, brothers, that what has happened to me has really served to advance the gospel, (13) so that it has become known throughout the whole imperial guard and to all the rest that my imprisonment is for Christ. (14) And most of the brothers, having become confident in the Lord by my imprisonment, are much more bold to speak the word without fear. (15) Some indeed preach Christ from envy and rivalry, but others from good will. (16) The latter do it out of love, knowing that I am put here for the defense of the gospel. (17) The former proclaim Christ out of selfish ambition, not sincerely but thinking to afflict me in my imprisonment. (18) What then? Only that in every way, whether in pretense or in truth, Christ is proclaimed, and in that I rejoice. Yes, and I will rejoice,
Being in a prison in the first century is much like today in the fact that it carries a certain social stigma. Many shy away from someone who has been in prison or who is currently serving a prison term. But this was not the case with Paul. The Philippian believers had every opportunity to turn their backs on Paul as he sit in that Roman prison. But the believers in Philippi remained friends, true and faithful to Paul.