What does Romans 10:18 mean?

Paul wrote in verse 16 that "they" have not obeyed the gospel. He is likely referring to the Jewish people. Since the gospel calls us to believe in Jesus, a refusal to believe amounts to disobedience (John 5:39–40). In the following verse, Paul asserted that faith comes by hearing the word of Christ.

Now Paul asks if the reason they did not believe is because they did not hear about Jesus. Did they not hear the gospel? Paul says no, that's not it. The Jewish people, people in general, have indeed heard the good news about Jesus. Paul borrows language of Psalm 19:4 to assert that the voice, the words, of the teachers of the gospel has gone out to all the earth, to the ends of the world.

Psalm 19 is describing not the revelation of the gospel of Christ, but the revelation of God's glory and creative power in nature. Paul began this letter by echoing Psalm 19 in declaring that God has made Himself knowable to humanity by what He has made (Romans 1:19–20). Here, though, Paul insists that God is making Christ Himself known to the world through the preaching of the gospel.

Does Paul mean that, by this point in history, literally every person on earth has heard the good news of Jesus? That's clearly not his intent. He seems to mean, more generally, that the gospel is in the act of being communicated to the known world. This is not an obscure message, so there is no reason Israel can claim to be ignorant of it. Paul likely also means that the people of Israel, specifically, have heard the gospel of Jesus from Christ Himself. Also, His followers had been preaching the message in Jerusalem and around Israel for more than 20 years by time this letter was written.