What does Romans 10:13 mean?

Paul quotes from the prophet Joel in this verse, declaring that everyone who calls on the name of the Lord will be saved (Joel 2:32). In doing so, Paul accomplishes two things. First, he connects this truth to His statement in the previous verse that Christ, the Lord of all, gives His riches to all who call on Him, both Jews and Gentiles.

The idea of "calling on the name of the Lord," in this context, means those who turn to Christ in faith seeking salvation. While not literally a description of a "sinner's prayer," Paul is referring to those who express the sentiment that a "sinner's prayer" contains. This is the act of placing one's faith in Christ. This is crucially different from those Jesus described in Matthew 7:21–23, as those who use His name, but have no actual faith in Him.

Paul makes a second connection, as well, showing that Christ the Lord is in fact Israel's Yahweh from the Old Testament. They are one in the same. All who call on Him in faith, both Jew and Gentile, will be saved from God's wrath against sin and will share in God's glory forever.