As Peter travelled through the land he was given power to perform many miracles so that many believed in the Lord. When Tabitha, a woman of many good works, died in Joppa they sent for Peter and he raised her from the dead.
While Peter was in Joppa the Lord sent an angel to Cornelius, a Roman centurion, to call for Peter. Meanwhile Peter was given a vision from the Lord preparing him to go to the gentiles, in the home of Cornelius. When he had preached about Christ unto them the Holy Ghost also came upon them. Then Peter understood that the gospel was also for the gentiles and baptized them.
So God showed that there is no difference between the Jew and the Gentile, but that he would continue to build His church, among both Jew and Gentile, even today.