stunned at repentance and life

When they heard these things they fell silent. And they glorified God, saying, “Then to the Gentiles also God has granted repentance that leads to life.”

Acts 11:18

This moment when the gospel advanced to the Gentiles was one of the most controversial and difficult times in early Christianity. There was a movement in Jerusalem to tentatively consider Gentiles into the church, but only those who first converted to Judaism and submitted to the covenant sign of circumcision. The foremost proponents of this movement (see Acts 11:2) were known as "the circumcision party" (which would not be a party I'd want to attend, by the way) and they confronted Peter after his return from Caesarea where he baptized the household of Cornelius.

These people were the first Jewish Christians to critically examine, hear, and accept Peter's report on Gentile conversion in full. It is clear that the Holy Spirit was at work, for the people most inclined to NOT accept Gentile conversion as Peter saw it in Caesarea were simply stunned into worshipful, agreeable silence once they heard what God had done. Salvation for Gentiles was settled, even if the issue of Judaizing them did not go away in the first century.

They clearly saw three undeniable truths in Cornelius' conversion: 1) God did the drawing. God did this dramatically and specifically, sending the lead apostle to a Gentile household, preparing both Cornelius and Peter beforehand, to bring and accept the gospel message. 2) Cornelius and his Gentile household repented. They turned from sin to Jesus as Savior. Their baptisms proved that they identified with Christ and His Church. 3) These Gentiles were born again into new life, evidenced by the Holy Spirit clearly among and in them. 

All the means and evidences of salvation that the church in Jerusalem proclaimed had been shown to and among the Gentiles. God was moving the gospel to the world. They were witnesses of this even as they witnessed to their culture of the saving work of Christ. And now the gospel was free to go to the world. There would be no stopping it.