Luke has shown us how the gospel went from Jerusalem to Judea to Samaria. Now, a third of the way into his book, he is ready for the crucial transition: the gospel is about to go to the Gentiles. This is a tremendous breakthrough. Today, of course, we can actually ask "Will the Jews be saved?" But in the first century, the really astonishing question was "Will the Gentiles be saved?" To even ask the question was borderline absurd. The only way Gentiles could be saved by Israel's God was by becoming Israelites. That is, Gentiles as such simply could not be saved. They could only be saved as Jews. Luke was well aware of this prejudice. For centuries, tradition has held that he was a Gentile. More recent commentators actually now think that he was a Jew, meaning that the entire Bible, so far as we know, was written by Jewish men. But regardless (both sides are guessing), Luke lived in the first century and he knew that Gentiles couldn't be saved. That's why this episode is the longest narrative in Acts (unless you count the voyage at the end of the book), and the key scenes in it are told three times. The point is clear, and made in so many words by Peter: God orchestrated the coming of the gospel to the Gentiles so that they could repent and be saved as Gentiles, without becoming Jewish or submitting to the Levitical system in any way.
