What does Acts 10:29 mean?
Two days prior, Peter had been praying on a rooftop in Joppa. God sent a vision explaining that the food restrictions in the Mosaic law have been lifted. Peter knew this, in some ways (Mark 7:19), but hadn't yet had an opportunity to test his convictions. Despite God's insistence, he was still reluctant. Even so, when three men, at least one of them a Gentile, arrived at the house, he invited them in and left for Caesarea Maritima the next day, as the Holy Spirit commanded him (Acts 10:9–23).Again vaguely, Peter understands that the vision was only ostensibly about food. "Without objection" mirrors the Spirit's command to leave "without hesitation" in Acts 10:20. Peter didn't hesitate time-wise and he didn't object or otherwise show any reluctance. The Holy Spirit hasn't told him what is going on; for all he knows, this centurion is going to crucify him, as Jesus prophesied (John 21:18). So he asks why Cornelius has called him.
Cornelius explains that he, too, heard from the Lord. An angel told him to call on Peter to hear what Peter had to say (Acts 10:1–8). What Peter has to say is that the Lord Jesus was crucified, buried, and rose again, and anyone who declares allegiance to Him will be forgiven of their sins. To Peter's shock, while he is still speaking, the household of Gentiles believe and receive the Holy Spirit. Peter doesn't even have to lay hands on them (Acts 10:34–48). Two men receive cryptic orders from God without explanation. Both follow the instructions immediately. Suddenly the gospel is open to the Gentiles en masse and the scene is primed for the arrival of the apostle Paul and his ministry to the Roman world.
Acts 10:24–33 describes the onset of the last step of Jesus' command for the disciples: to share His story in Jerusalem, Judea, and Samaria, and to the ends of the earth (Acts 1:8). Upon an angel's prompting, a Roman centurion named Cornelius has sent for Peter. Meanwhile, the Holy Spirit has been teaching Peter that Gentiles are no longer unclean (Acts 10:1–23). Peter will go to Cornelius and bear witness of Jesus. Everyone in earshot will believe Peter and receive the Holy Spirit (Acts 10:34–48). The way will be open for Paul's ministry in Syria, modern-day Asia Minor, Macedonia, Greece, and Italy.
Peter has been a dominant voice in the spread of Jesus' message to Jews and proselytes. Now he brings the gospel to Gentiles. An angel tells Cornelius, a centurion, to ask Peter to come to him. Peter is praying when he receives a vision of food—including non-kosher food—and God's voice telling him to eat. When the centurion's messengers arrive, Peter realizes the dream meant that Gentiles are no longer unclean. He follows the messengers and tells Cornelius' household about salvation through Jesus. Before Peter can lay his hands on them or baptize them, the Holy Spirit falls on them.