What does Romans 15:33 mean?

After asking his readers to wrestle with him in prayer about his own serious circumstances, Paul closes the formal part of his letter with a prayer for them. This was a customary greeting among believers of the time, but we should not read it as anything less than a genuine prayer for the Christians in Rome.

Paul prays that the God of peace would be with them all. "God of Peace" is one of the titles Paul uses to describe God's nature. He is the God who gives peace in every sense of that word. He makes us to be at peace with Him through faith in Christ (Romans 5:1). He gives us peace in our hearts and minds through His Spirit (Romans 8:6). And He makes it possible for us to be at peace with other Christians (Romans 14:19).

Paul's letter isn't entirely finished. In Romans chapter 16, Paul launches into a series of post-script greetings and recommendations, followed by more instructions and greetings, before coming to a beautiful letter-closing doxology or hymn of praise to God.