"The next day, as they went on their journey and drew near the city, Peter went up on the housetop to pray, about the sixth hour. Then he became very hungry and wanted to eat; but while they made ready, he fell into a trance and saw heaven opened and an object like a great sheet bound at the four corners, descending to him and let down to the earth. In it were all kinds of four-footed animals of the earth, wild beasts, creeping things, and birds of the air, and a voice came to him, 'Rise, Peter; kill and eat.' But Peter said, 'Not so, Lord! For I have never eaten anything common or unclean.' And a voice spoke to him again the second time, 'What God has cleansed you must not call common.' This was done three times. And the object was taken up into heaven again" (Acts 10:9-16).
As the messengers from Cornelius neared Joppa where Peter was staying, Peter prayed to God privately while his host prepared a meal around noon. While he was praying, he fell into a "trance" (i.e., a state of partial consciousness) and had a vision. In the vision he saw something that looked like a large linen sheet, secured at the corners, with a variety of creatures inside. According to the standards of the Mosaic law, some of the animals therein were unclean and not authorized for consumption by Hebrews (cf. Lev. 11). Peter was well aware of this fact and resisted the voice that spoke to him and encouraged him to partake. Peter felt strongly enough about this subject that he was willing to contradict what the Lord commanded. Typical Peter!
Although he was hungry, Peter had no intention of killing any animal for food that was deemed unclean by the Law of Moses. He would not just rise and eat both clean and unclean animals indiscriminately, as if there was no difference between the two. God spoke to him a second and even a third time, pressuring him to eat. Peter resisted each time, but God replied with a statement that would give Peter a lot to think about in the coming days - "What God has cleansed you must not call common." Since the Old Law had been abrogated at the cross, the Jewish dietary restrictions were no longer in place (but this was not yet understood by the Jewish Christians). Certain creatures that were once forbidden foods are now acceptable for God's people. The apostle Paul later makes this point crystal clear when he wrote - "Having wiped out the handwriting of requirements that was against us, which was contrary to us. And He has taken it out of the way, having nailed it to the cross. Having disarmed principalities and powers, He made a public spectacle of them, triumphing over them in it. So let no one judge you in food or in drink, or regarding a festival or a new moon or Sabbaths, which are a shadow of things to come, but the substance is of Christ" (Col. 2:14-17; cf. I Tim. 4:3,4).
But, beyond this physical cleansing pertaining to animals, there is a much deeper spiritual meaning that will be revealed as the events of Acts 10 continue to unfold. The timing of this vision right before the arrival of Cornelius' servants is no coincidence. God is preparing Peter to learn a great lesson about Gentiles and their suitability as recipients of the gospel message (cf. Mark 16:15,16; Acts 1:8), but it will be a challenging lesson for him and the other Jewish Christians to fully embrace due to culture and habit. Jews considered Gentiles to be unclean, and lifelong prejudices are hard to shed.
After Peter rejected the animals for the third time (cf. Gen. 41:32), they were taken back up into heaven again and the vision ended. Peter is puzzled by the meaning of the vision but will figure it out soon enough.