What does Philippians 1:25 mean?
Paul doesn't merely hope that he will remain alive to continue ministering. He is "convinced of this." He gives two specific reasons why he feels this way, as they apply to the Philippian believers. First, though the Philippian church was growing more and more mature, Paul could continue to serve them. His purpose is to assist the Philippians to great maturity. While it is not noted in the New Testament whether Paul ever returned to Philippi again, Paul appears confident he would return (Philippians 1:26).Second, Paul would remain for their "joy in the faith." Faith involves both growth and joy. First Peter 1:8–9 says, "Though you have not seen him, you love him. Though you do not now see him, you believe in him and rejoice with joy that is inexpressible and filled with glory, obtaining the outcome of your faith, the salvation of your souls." The continued presence of a man like Paul would certainly encourage the people he had been ministering to.
Philippians 1:19–30 shows Paul reflecting on two competing desires. On one hand, a believer wants to serve God and bring others to Christ through their life. On the other hand, a Christian yearns to leave suffering behind—to be with God in eternity. Paul concludes that it's better to live until God calls him home, so he can serve his fellow men. Paul also encourages the Philippians with his conviction that he will be released to see them again. His experiences, good or bad, are all adding to the glory of Jesus Christ.
In chapter 1, Paul thanks the Philippian believers for supporting his ministry. Even when Paul was jailed, or persecuted, they had been generous and loyal. Paul encourages these Christians by explaining that all of his suffering has been for a good cause. Even better, these attempts to persecute Paul have actually caused the gospel to spread. For this, Paul is grateful. He fully expects to be released, and to see the believers of Philippi again.