The disciples were all Jews. And til now, the gospel had been preached in the synagogues, reaching more Jews. It was generally thought that this new religion was a sect of Judaism.
In this passage, however, we see that this man named Cornelius - who was not Jewish - had been selected by God to be a convert to this new faith. Cornelius was righteous, much as Job was righteous. He did all the right things and prayed to God. He simply wasn't a Jew. But he was a son of Adam.
We also see that Peter had been selected to teach Cornelius. The Jewish dietary laws were very explicit. God had told them that certain things were clean or unclean for eating purposes. Peter, in his hunger, was shown a vision of many living creatures and told to kill and eat them. But he objected that he had never eaten anything unclean - ever. But God told him not to judge. That God can make anything clean.
Peter's physical hunger seems to have been a metaphor for God's hunger that all the world should know Him. God's overriding desire is that all men should be saved. Jesus said that the disciples would be witnesses to Him throughout all the earth.
As the spiritual descendants of the disciples, we should be witnessing, too. We should be witnessing to the pagan, the atheist, the deluded, the deceived, the murderer, the rapist, the robber - the entire world.
Let me be very clear here. We do not convert. That is the work of the Holy Spirit. We merely inform. We tell what we know. God will do the rest.
Teach us more of You that we may tell all the world around us. Keep us open to the movement of Your Holy Spirit and reign in our tendency to prejudge.
In Jesus' most precious name.