What does Acts 13:47 mean?

Paul is addressing a crowd of Jews and Gentiles who accept his message about Jesus and a group of Jewish leaders who do not. Here, he quotes the end of Isaiah 49:6. Many times, when a New Testament speaker quotes a portion of the Old Testament, they mean to bring to mind the rest of the passage. In Isaiah 49:1–2, God chooses His Savior, one with a "mouth like a sharp sword" (Isaiah 49:2; Revelation 19:15). In Isaiah 49:3–5, Israel refuses to return to God, so God tells His messenger, "It is too light a thing that you should be my servant to raise up the tribes of Jacob and to bring back the preserved of Israel" (Isaiah 49:6). God wants more than just the Jews; He wants the world.

Paul applies Isaiah 49:6 to the entire nation of Israel. God made a covenant that Abraham's descendants would bless the world (Genesis 12:3). They did so by providing the Messiah to the world, but they should have also introduced the Messiah to the world. God knew that wouldn't happen. Much of Paul's ministry involves telling the Jews about Jesus and building churches with the eavesdropping Gentiles who accept his message.

Simeon also quoted part of Isaiah 49:6 when he met the baby Jesus at the temple, but he added part of Isaiah 46:13, calling Jesus, "…a light for the revelation to the Gentiles, and for glory to your people Israel" (Luke 2:32). Paul's heartfelt wish, that Israel would accept its Messiah (Romans 9:1–5) will come true during the millennial kingdom. First, however, the Gentiles are invited in (Romans 11:25–27).