The next day, as they were on their journey and approaching the city, Peter went up on the housetop about the sixth hour to pray. And he became hungry and wanted something to eat, but while they were preparing it, he fell into a trance and saw the heavens opened and something like a great sheet descending, being let down by its four corners upon the earth. In it were all kinds of animals and reptiles and birds of the air. And there came a voice to him: “Rise, Peter; kill and eat.” But Peter said, “By no means, Lord; for I have never eaten anything that is common or unclean.” And the voice came to him again a second time, “What God has made clean, do not call common.” This happened three times, and the thing was taken up at once to heaven. Now while Peter was inwardly perplexed as to what the vision that he had seen might mean, behold, the men who were sent by Cornelius, having made inquiry for Simon’s house, stood at the gate and called out to ask whether Simon who was called Peter was lodging there. And while Peter was pondering the vision, the Spirit said to him, “Behold, three men are looking for you. Rise and go down and accompany them without hesitation, for I have sent them.” And Peter went down to the men and said, “I am the one you are looking for. What is the reason for your coming?” And they said, “Cornelius, a centurion, an upright and God-fearing man, who is well spoken of by the whole Jewish nation, was directed by a holy angel to send for you to come to his house and to hear what you have to say.” So he invited them in to be his guests. The next day he rose and went away with them, and some of the brothers from Joppa accompanied him. (Acts 10:9-23)
Peter, as a Jew, had been very careful to obey laws which clearly stated that certain kinds of food were unclean. Likewise he had avoided any contact with unclean non-Jewish people.
See how God prepares him to meet these men from the Roman army of occupation.
And see how the travellers arrive just as God finishes speaking to Peter.