When Peter returned to Jerusalem, the Jewish believers criticized him. They would have done that for the same reasons Peter would have before his vision of how all that God made clean is clean (in chapter 10). Peter now had a new understanding of who salvation was available to.
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Note that often believers are referred to as those circumcised and nonbelievers are referred to as those not circumcised. Sometimes Gentiles are referred to as not circumcised or non believers and the words are used interchangeably. Jews practiced circumcision and the early believers came from among the Jews, so they were circumcised. At this time the Gentiles did not practice circumcision but upon becoming believers there was a time that it was believed all Gentiles who became believers must be circumcised.
Very briefly, when circumcision first came to God's people it was with Abraham. God promised to care for him and fill the earth with his descendents. Abraham promised God would be his only God and he would follow him with his whole heart forever. Abraham would abandon the world and it's ways to live fully for God. It was a forever agreement between God, Abraham, and Abraham's descendants. The mark or seal of that covenant was Abrahams circumcision.
Later, Paul spoke to the church in Corinth as follows;
From article titled, Circumcision: The first major dispute in the New Testament church.
"Was anyone called while circumcised? Let him not become uncircumcised. Was anyone called while uncircumcised? Let him not be circumcised. Circumcision is nothing; and uncircumcision is nothing, but keeping the commandments of God is what matters." (1 Corinthians 7:19) St. Paul writes to the Corinthians:
The teaching became it was not circumcision nor non circumcision of the flesh that differentiated the believer from the non believer. Nor was it circumcision of the flesh that made a believer a follower of God but the circumcision of the heart toward God. Circumcision of the heart by shedding off the ways, traditions, passions, and temptations of the world.
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Back to chapter 11:
Paul was speaking with believers back in Jerusalem who still believed and followed the belief that some people were deemed clean by God while others were unclean. They still followed the Jewish belief that Gentiles were unclean and Jews were not to associate with them nor enter their homes. Peter stated those beliefs when he began speaking to Cornelius in chapter 10. They were upset Peter entered the home of Cornelius, a Gentile, and beyond that, ate with him and his people.
Again, the story of his trance and dream of the sheet with all sorts of creature in it and how he was told to not call anything unclean that God has made clean was told by Peter.
Peter continued with his encounter with the men sent to Joppa by Cornelius. Again, the vision Cornelius had instructing him to summon Peter to his home to bring the message of salvation from God to him and his household was shared.
Peter continued by telling those who were accusing him of doing wrong that he witnessed the Holy Spirit fall on Cornelius and those gathered with him, just as it had fallen on Peter and the believers in the very beginning. Peter said that when that happened, he thought of the words of the Lord when He said, "John baptized with water, but you will be baptized with the Holy Spirit."
Peter addressed their concerns by saying, "And since God gave these Gentiles the same gift He gave us when we believed in the Lord Jesus Christ, who was I to stand in His way?" When all who were gathered heard that they stopped objecting to what Peter had done with the Gentiles and began praising God with a new understanding that God had also given the Gentiles the privilege of repenting of their sins and receiving eternal life.
In chapter 7, we read of the stoning of Stephen and the scattering of the beleivers. We then read of Saul's persecution of the believers in chapter 8 and his conversion to becoming a believer in chapter 9. This series of events ended with Saul in Damascus preaching about Jesus in such a powerful way that the religious leader plotted to kill him. He then escaped to Jerusalem and preached there in powerful ways. This time he debated with some Greek speaking Jews who then plotted to kill him. He was helped by the believers to get back to his home town of Tarsus.
That reminds us of how the believers came to be scattered and how Saul ended up back in Tarsus. Now back in chapter 11, we read of the believers being scattered to many places and that in those places they preached the word of God. Some that went began preaching to the Gentiles and saw a large number of them turn to the Lord.
When the church in Jerusalem heard all that was happening, they sent Barnabas to Antioch and upon his arrival, he was filled with joy by witnessing the evidence of God's blessing. He encouraged the believers there to remain true to God. Barnabas was described as a good man, full of the Holy Spirit and strong in faith. We are told many people were brought to the Lord.
We can see how the word of God, the truth of Jesus, and the Good News of salvation was spread because of the persecution of believers.
Barnabas then went to Tarsus to retrieve Saul. He found him and took him back to Antioch and both of them stayed with the church for a year teaching large crowds of people. It is noted in verse 26 that it was in Antioch at that time, the believers (or in the Greek, "disciples") were first called Christians.
Agabus traveled to Jerusalem with some other prophets. During one of the meetings, he stood up and guided by the Spirit, predicted a great famine that would overtake the entire Roman world during the rein of Claudius. Hearing that, the believers in Antioch sent relief to the brothers and sisters in Judea by giving as much as they could. They sent their support with Barnabas and Saul who were to take it to the elders of the church in Jerusalem.
(Another note: this was the first time elders in the church were ever mentioned.)