Luke explains in this chapter, how the evangelism was accelerated because of the persecution, Jesus warned his followers that they would reach moments of anguish and persecution, because, persecution is the favorite reaction of the devil to the proclamation of the gospel, especially when people are accepting it and God is working wonders.
The pace of the persecution and attacks on the church had increased since the arrest of Pedro and Juan after the healing of the crippled crippled man, the stoning of Esteban had put an end to the restrictions and fears that the leaders had about reaching out to the followers of Jesus. Now the time had come to fire against the flock of the Lord, but Satan's tactics failed him, because the scattering of the Christians only served to spread the flame of the message of Jesus Christ everywhere, Luke says that everywhere they arrived They announced the gospel and the revival progressed more and more.
The immediate effect of the terror campaign was the opposite of what Jewish community leaders expected. Thus the gospel reached places it would never have reached if all those believers had not been forced to leave their homes.
God used the persecution in Jerusalem to set in motion his plan for the fulfillment of the great commission, for God has his own methods to mobilize his people.