Paul here identifies himself as the prisoner of Christ Jesus. At this point, Paul is most likely in prison in Rome so he is truly a prisoner. And he is in prison for preaching this gospel that declares that Jesus died for all people, both Jews and Gentiles, and both are saved through His blood. Thus Paul is in prison for the sake of or because of the Gentiles to whom he preached this good news.
Not all of us will be put in prison for sharing our faith with others but all of us are called to share our faith. Are you willing to go to prison in order that someone else might hear the gospel of Jesus? Are you willing to be inconvenienced so that others can receive the free gift that God provides for them? Are you willing to go out of your way to be the one to deliver that message?
It’s fine and dandy to say yes to those questions, but are you doing that? Can you point to persecution in your life for the sake of the gospel? Are you regularly inconvenienced and do you got out of your way to make sure others hear and understand and receive God’s message?
Lord, help us to be willing to go as far as you lead us to see people saved. Help us to be all things to all people so that by all means some might be saved!