What does Romans 11:3 mean?

Paul is debunking the idea that God has rejected His people Israel. For one thing, Paul wrote, he himself is an Israelite and God has not rejected him. Instead, by God's grace, Paul has come to God through faith in Christ as an Israelite. To show that there are others, Paul now quotes from a conversation between God and the prophet Elijah.

Elijah, discouraged from standing alone against those who worshiped Baal, said the words of this verse in 1 Kings 19:10. His complaint was against God's people Israel. They had killed the other prophets of God. They had destroyed the altars used for making legitimate offerings to God. Elijah believed he was the only one left still faithful to the Lord, and they wanted to kill him, too. Elijah was convinced he was speaking of all the other Israelites on the planet. Everyone else has turned away from God and to the worship of Baal.

God showed Elijah that this was not true. Paul, too, will show that a remnant of Israelites has remained faithful to God by having faith in Christ.