We are introduced to a centurion soldier named Cornelius. A centurion was usually in charge of 100 men and were considered the backbone to the Roman army. Being a devoted man of God, Cornelius was known for the charitable things he did around his city.
Cornelius had a vision where he saw an angel of the Lord. The Lord wanted him to send a message to Joppa to invite Peter to his house. Because Cornelius was devoted to the Lord he immediately sent three men out to get Peter. I am sure he was very anxious for Peter to arrive after all he had heard about him.
After a long morning of preaching Peter went to the roof of his host home to pray while the people prepared the food. He fell into a trance while he was up there. It could have been that he dozed off or was wide awake and saw everything with his eyes, either way the message was from God. In the vision he saw what looked like a sheet and in it were all kinds of animals clean and unclean based on the Old Testament laws. Look at Lev. 11 for more description of these animals. To put it plainly the Lord told Peter, "you are hungry so here is some food." Peter didn't want to eat them because they were unclean and even the animals that were considered clean had been defiled by the others. God told him that what He had made clean was clean and not to dispute Him. The purpose behind this vision was to prepare Peter for his encounter with Cornelius. In these cities and neighboring countries there had been so many prejudices against people just because where they were born. God wanted Peter to realize that man was never to be considered unclean because when He created man He looked at him and considered it good. After Peter had seen this vision three times the objects returned back into the sky.
After having this vision there was a knock at Peter's door and there stood Gentile soldiers. Remembering what the Lord had told him he invited them in and gave them food and shelter for the night. Now you have to understand that Peter who was a Jew had been taught his whole life the Gentiles were "unclean" and were an abomination to the Lord. But by God's grace those barriers were being broken down and he was showing them love.
Peter leaves his home and sets out on his journey toward Cornelius' house. Based on the text it would seem that Peter didn't know why he was being summoned but he went anyways. Once he arrived he was greeted in a humble way by many of the people from the city. Cornelius wasted no time in telling him about the vision he had seen from the Lord and wanted Peter to tell them all he knew.
Peter begins to preach to the Gentile crowd of how he serves a God who loves everyone. He tells them all that he had witnessed and how even those who were in Jewish leadership turned against Him and hung Him on a cross While he was preaching the Holy Spirit fell on the crowd because of their willingness to listen. Everyone was amazed and they decided that they also all needed to be baptized as well. Wanting to know more they asked Peter to stay longer and continue to preach to them.