What does Romans 10:12 mean?

Paul has made clear throughout Romans that the only way to be declared righteous by God is through belief—through faith in Christ. He has written so again in the previous verse, quoting Isaiah 28:16 to show that everyone who believes in Christ will not be put to shame. That is, all believers in Jesus will be vindicated in the end. Paul noted that the Scriptures clearly stated that everyone who believed would be so protected.

Now Paul clarifies that by "everyone," he truly does mean everyone. For Israelites, the world was ever and always divided into two categories: Jews and Gentiles. Those on the "inside" with God, and those on the "outside." Paul has expressed his profound grief that so many Israelites still cling to this false idea (Romans 9:1), applying it in ways which God never intended. Paul has declared his ongoing prayer that his own people the Jews will be saved (Romans 10:1).

Now he writes forcefully once more that there remains absolutely no distinction between Jews and Gentiles—using the term "Greeks" here—when it comes to being declared righteous by God through faith in Christ. After all, the same Lord is Lord of all people. By Lord, Paul is referring to Jesus, the Christ. He rules over all people, both Jews and Gentiles. In fact, the Lord gives His riches to all who call on Him. Paul wrote something similar in Romans 3:29–30.

Implied in Paul's statement is the idea that Christ is listening, that He will receive anyone who calls on Him in faith, no matter their nation or the circumstances of their birth. He is not reserving salvation only for those who are part of a certain heritage.