The lectionary passage focuses on a small portion portion of this chapter, but I will focus on the entire Cornelius story.
The chapter begins with Cornelius. He is a Roman centurion who loves God and gives alms. But he is not a Jew. It seems God has already begun to work on spreading the Gospel without the help of the Apostles in the case of Cornelius. But in a vision, God tells Cornelius to send for Peter. Unbeknownst to Cornelius, God has also given a vision to Peter. Peter is a good Jew who has probably never sat down at a table to eat with a Gentile.
I have to laugh at Peter's answers to God. Peter knows it is God speaking. God sends a sheet of unclean animals and he tells Peter to eat them. Peter replies that he has never eaten what is unclean. Why would God tell Peter to do something God commanded people not to do in the Torah? This passage speaks heavily about the importance of experience. The Wesleyan tradition of which I am a part emphasizes experience must go along with Scripture. If Peter had screamed "I only listen to the Torah, not God," then we Christians would be practicing Judaism.
This passage also teaches us that God has no favorites. Really? This is one of the hardest lessons to grasp. Nothing I can do can make God love me more or less.