"So they shook the dust from their feet in protest against them and went to Iconium." NIV translation
Instead of quarreling with the religious leaders and others that were persecuting them, Paul and Barnabas left and went to Iconium which is in the modern country of Turkey. They put the situation in God's hands as they "shook the dust from their feet". That is a good pattern for us as well when people start to argue and persecute us. We too must give all situations and people over to God and realize that only he has the power to change people.
"And the disciples were filled with joy and with the Holy Spirit." NIV translation
Joy and the Holy Spirit; Does that describe your life in Christ? In the face of persecution, the disciples were filled with joy because they were focused on God and his eternal perspective. When things get difficult (and they will if you are following Jesus), that is when you have the opportunity to demonstrate the power of God in your life. Others can see that your joy is not affected by your situation.