John Piper helps us understand Peter’s vision in Acts 10, in a sermon, “What God Has Cleansed Do Not Call Common”:
Let me try to sum up the whole story for us. Cornelius is a Gentile, not a Jew. But he feared God as best he knew him and he prayed and he gave alms and walked in an upright way (10:2, 22). God sent an angel to him and told him to send for Peter to hear what he has to say.
At about the same time God gave Peter a vision of animals that the Jews regarded as unclean because of the ceremonial law of the Old Testament. The voice from heaven said, “Rise and eat.” But Peter protested that they were unclean. And the voice came back with these decisive words in verse 15: “What God has cleansed you must not call common!”
In other words, with the coming of Jesus into the world and with the final cleansing sacrifice of Christ now offered and with the command to take the gospel to all ethnic groups in the world now given, the old ceremonial laws about foods are lifted and that barrier to the Gentile world is removed.
And so Peter’s vision has two points: the food laws are fulfilled and ended in Jesus (Mark 7:19), and the people they kept you separate from (the nations, the Gentiles) are not to be considered unclean or common.