The story of Cornelius and Peter is super important. It is the crux of the realization that God’s kingdom is available to whole world instead of just the Jewish people.
Jews are God’s special people for the expressed purpose of showing the world what God is like and being living examples of the kind of humanity God wants the world to live. Israel had had this vocation for quite some time (all the way back to the Exodus… even the patriarch Abraham).
To a Jew the world was divided into two categories: Jews and non-Jews (or Gentiles).
Peter’s vision of unclean food now being clean and the evidence of the Holy Spirit on Cornelius’ household was a realization for Peter (thus the whole, young Jesus movement) that Jesus died and rose again not just for God’s special people, Israel, but actually the entire world.
This application of the efficacy of Jesus sacrifice has huge implications from this point forward, not the very least being Gentiles can be saved from judgment, too!!