What is the meaning of Romans 1:8?

8 First, I thank my God through Jesus Christ for you all, that your faith is spoken of throughout the whole world. (Romans 1:8 KJV)

William Burkitt’s Commentary

Observe here, 1. The great and wonderful success of the gospel; it had produced faith in the hearts, and obedience in the lives of the Romans, which had made them famous throughout the world:  Your faith, says the apostle,  is spoken of throughout the whole world; that is, through all the Roman empire, which at that time ruled over a great part of the known world. The entertaining of the gospel in Rome made that place more celebrated and famous than all the victories and triumphs of the Roman emperors; faith and holiness make a place and people more renowned than all outward prosperity and happiness.

Observe, 2. That this their renowned faith was the ground, yea, the highest and chiefest ground of the apostle’s rejoicing;  First, I thank my God, that your faith is spoken of throughout the whole world.

Learn thence, That it is both the duty and the disposition of the faithful ministers of Jesus Christ, to be highly thankful to God, above all things, for the powerful success of the gospel, in bringing sinners to the faith and obedience of Jesus Christ. This is our rejoicing, or rather, this will be our crown of rejoicing on the day of Christ: We value our lives only by their usefulness to the souls of our beloved people; we live as we see some of you stand fast in the Lord; we die as we see others stick fast in their sins.