What does Philippians 1:13 mean?

This advance of the gospel, mentioned in verse 12, included even the guards who were part of Paul's Roman imprisonment. The imperial guard was literally the praitorion: soldiers assigned to guard high–ranking officials in Rome, who now had some exposure to Paul's teachings. Paul's captivity gave him the opportunity to interact with these men on a regular basis. As a result, many of them had been converted. It was of great significance that some of the most revered soldiers of Rome had become followers of Jesus.

In addition, Paul mentions "all the rest." This is likely a general reference to both Jews and Gentiles living in Rome who heard about Paul's gospel message. Acts 28:30–31 says of Paul, "He lived there [Rome] two whole years at his own expense, and welcomed all who came to him, proclaiming the kingdom of God and teaching about the Lord Jesus Christ with all boldness and without hindrance."

Critically, Paul notes that these people are all aware that he is a prisoner for one reason only: his witness for Christ. Neither the guards, nor "all the rest," are under any illusions. Paul is no criminal or rebel. He is guilty of nothing more or less than preaching the gospel.