What does Romans 11:13 mean?
Paul has been writing about God's relationship with His chosen people, Israel. He described how and why God hardened most Israelites to faith in Christ. God's purpose was, in part, to include Gentiles—non-Jews—in the promise of salvation through faith in Christ. In the previous verse, Paul introduced the idea that at some point in the future, the full inclusion of Israel to faith in Christ will result in great things for all people.Now Paul addresses Gentiles directly, beginning a thought he will complete in the following verse. Paul describes his identity and purpose to be an apostle to the Gentiles. Christ Himself gave this role to Paul in Acts 9:15. Paul writes that he magnifies his ministry to take the good news about faith in Jesus to all Gentiles. In other words, he glorifies his ministry. He goes big. He works hard at it. He is bold and strategic and amplifies the message of God's grace for the Gentiles through faith in Christ.
In part, as Paul reveals in the next verse, he does this to provoke jealousy among his own Jewish people. He wants to see them saved, to have the same special relationship with God that the Gentiles have now received.
Romans 11:11–24 describes why God has hardened Israel in her unbelief in Christ. It is to make room on God's figurative olive tree for the Gentile Christians. The old branches of unbelieving Jews have been broken off for now, and the new branches have been grafted in to the root. In turn, the salvation of so many Gentiles will provoke Israel to jealousy, drawing her back to God through faith in Christ when He removes the hardening of her unbelief. When that happens, after enough Gentiles have believed, the old branches of Jewish believers will be grafted back into the tree.
In Romans 11, Paul concludes his exploration of God's plan for His chosen people Israel. It's true that as a nation, Israel has rejected faith in Christ, but a remnant of Israelites has believed in Jesus. God has hardened the rest in unbelief, but will bring Israel back to faith when enough Gentiles have come to Him through Christ. Then many Israelites will trust in Christ, as well, and God will renew His covenant with His people. Paul concludes this section with a powerful poem or hymn about God's independence and how He is beyond our full comprehension.