"They arrived at Ephesus, where Paul left Priscilla and Aquila. He himself went into the synagogue and reasoned with the Jews. When they asked him to spend more time with them, he declined. But as he left, he promised, 'I will come back if it is God's will.' Then he set sail from Ephesus." NIV translation
So the group made their way to Ephesus and Paul once again preached in the synagogue. This time they wanted to hear more but Paul did not stay. This may seem strange but evidently God had placed on his heart to travel to other places. He left Priscilla and Aquila there to tend the believers and went on his way.
Now, we see why Paul kept moving and what God had placed on his heart. Instead of staying in one place he traveled around strengthening the groups of believers. Although it would have been good to stay in Ephesus with his fellow workers, Paul knew that it was best to travel to all of these groups and build them up in the faith.
This is a good lesson for us in that we too must constantly seek the face and will of God so that we do not settle for what is good but trust and obey God knowing that He knows what is best.
"Meanwhile a Jew named Apollos, a native of Alexandria, came to Ephesus. He was a learned man, with a thorough knowledge of the Scriptures. He had been instructed in the way of the Lord, and he spoke with great fervor and taught about Jesus accurately, though he knew only the baptism of John. He began to speak boldly in the synagogue. When Priscilla and Aquila heard him, they invited him to their home and explained to him the way of God more adequately." NIV translation
This passage introduces us to a Jewish man who accepted Christ and went about sharing that faith with others. We are told that he had a thorough knowledge of the Old Testament but we are not told who taught him or how he came to accept Christ. God was using him and his teaching was accurate but lacking as he only spoke of the water baptism (repentance and forgiveness). Priscilla and Aquila heard him speak and noticed that he did not speak of the Spirit and so they invited him to their home and taught him. The teaching about the Spirit was crucial as that is the power given us to walk the walk of faith. (Remember that Jesus told the disciples that they "will receive power when the Holy Spirit comes on you" (Acts 1:8). Apollos was humble enough to listen to the instruction and correct his teaching. Even today, there are many whose teaching is lacking as they do not teach about the Spirit. We, like Priscilla and Aquila, have a duty to tell them the truth and we can follow their example in that they did so in private.
"When Apollos wanted to go to Achaia, the brothers encouraged him and wrote to the disciples there to welcome him. On arriving, he was a great help to those who by grace had believed. For he vigorously refuted the Jews in public debate, proving from the Scriptures that Jesus was the Christ." NIV translation
Achaia is the southern part of Greece and, after Apollos received the knowledge from Priscilla and Aquila, he wanted to go and share it there. He was able to debate the Jews there and prove to them from the Old Testament that Jesus was the promised Messiah.