What does Acts 10:23 mean?
Verse divisions were not part of the original Scriptures, and some traditional choices are awkward. For the sake of clarity, it would have been better if this verse was split—there are two distinct moments in question. Peter has had a vision wherein God repeals the Mosaic law regarding clean and unclean food. Right before Peter had this vision, he had been waiting for a meal from the household of his guest, Simon the Tanner (Acts 10:9–16). Right after the vision, three strangers come to the gate asking for Peter. At least one of them is a Gentile, since he is a soldier of the Italian cohort (Acts 10:1, 7, 17).The timing is not coincidental. God told Peter that foods were no longer unclean, and now three "unclean" men arrive, at meal time. Peter understands God to say He is repealing any custom against eating with Gentiles, as well. Although Peter accepts this now, he and other Jewish Jesus-followers will have problems, later. Jews will find it incredibly difficult to eat with their Gentile brothers and sisters if the Gentiles don't follow kosher law. James, the half-brother of Jesus and the leader of the Jerusalem church, will convene a meeting with the church leadership, and they will decide that for the sake of peace, Gentiles should "abstain from what has been sacrificed to idols, and from blood, and from what has been strangled" (Acts 15:29). Paul will later ignore the rule against eating food sacrificed to idols—possibly because in cities outside of Jewish territory, it is difficult to find meat that hasn't been so tainted. But he admonishes Gentile believers to abstain if it bothers others (1 Corinthians 8).
Still, it is difficult to change such a deep cultural tradition. Paul will make his headquarters in the Gentile city of Syrian Antioch, and when Peter visits him there, they will all eat together with no problem. But when more-legalistic Jewish Jesus-followers come from Jerusalem, Peter and Barnabas will withdraw from eating with the Gentiles. Paul will call them out publicly for their hypocrisy (Galatians 2:11–14).
It's interesting that some of the Jewish Jesus-followers from Joppa go with Paul and Cornelius' messengers. Some of their motivation is, no doubt, curiosity. But it's also interesting that throughout Peter's travel in Lydda and Joppa, there is no mention that Peter has a companion from Jerusalem (Acts 9:32–43). In his previous work, the apostle John was almost always with him. When Philip shared Jesus' story in Samaria, Peter and John went to affirm the Samaritans understood. They laid their hands on the people, and the people received the Holy Spirit (Acts 8:4–17).
In Lydda and Joppa, Peter is visiting with Jews who are already confirmed Jesus-followers; they may have received the Holy Spirit in Jerusalem before Saul started his persecution (Acts 8:1–3) or they may have learned from Philip when he traveled from Azotus to Caesarea (Acts 8:40). But now, Peter is called to Caesarea, to a Gentile, and he will need witnesses for what is about to happen. When Peter returns to Jerusalem, the legalistic Jesus-followers will question his choice to eat with "uncircumcised men." Although they seem to accept Peter's lone testimony, he also brings the six men from Joppa (Acts 11:1–18).