What does Romans 1:9 mean?
Paul has just declared how he thanks God for his readers, the Christians in Rome (Romans 1:8). Now he calls on God to be his witness about what he is about to say to them. In other words, Paul wants to make it abundantly clear that he isn't lying to them. If God chose to speak about this, Paul says, He would back me up.Paul is not being frivolous or light-hearted about God, either. He adds that he serves God with his spirit in proclaiming of the gospel of God's Son Jesus. In other words, serving God by preaching Christ is Paul's whole life. He is being absolutely serious when he says that God would back him up on what he is about to say.
And what Paul is about to say is that he prays something about his readers, the Christians in Rome, "without ceasing." In this case, we should take "without ceasing" to mean "regularly and continually." This does not mean literally every second of every waking moment, of course. Rather, it implies that Paul does not take days off from praying for this thing, and it is important to him that his readers understand that. The following verse reveals what it is that he asks God for.