What does Romans 1:8 mean?

Having completed the opening greeting of his letter (Romans 1:1–7), Paul launches into some personal words to the Christians in Rome. His letters to Christians and churches in various cities often begin with a declaration of his gratitude for those to whom he is writing.

The reason for Paul's thankfulness for the Romans is that their faith is proclaimed in all the world. In other words, the Christians in Rome have become famous far and wide for believing in Jesus. This is exactly Paul's mission in life, given to him by Christ Himself: to see belief in Christ spread to all the nations of the world (Romans 1:5). So, it is not surprising to hear him thank God through Jesus Christ for this.

We should take note of Paul's prayer life. He is modeling for us that prayers to God, including giving thanks, happen through Jesus. Most Christians have formalized this practice by ending our prayers with "in Jesus' name." We do this because our access to God the Father is possible only because we are "in Christ." We could never approach God on our own, in our sin, without Christ.