18 After this, Paul stayed many days longer and then took leave of the brothers  and set sail for Syria, and with him Priscilla and Aquila. At Cenchreae he had cut his hair, for he was under a vow. 19 And they came to Ephesus, and he left them there, but he himself went into the synagogue and reasoned with the Jews. 20 When they asked him to stay for a longer period, he declined. 21 But on taking leave of them he said, “I will return to you if God wills,” and he set sail from Ephesus.
22 When he had landed at Caesarea, he went up and greeted the church, and then went down to Antioch. 23 After spending some time there, he departed and went from one place to the next through the region of Galatia and Phrygia, strengthening all the disciples. (Acts 18:18-23 (ESV)
So aside from Priscilla and Aquila going with Paul as he returns to Antioch, the curious thing in here is the vow that Paul takes. This would be the vow of a Nazarene which requires a person to cut his hair at the beginning and not drink wine or cut his hair again until the vow was over. This was the vow that Samson had been born into, a Nazarene from birth.
The Book of Acts covers a time of transition between the Old and the New Testament. During this time Christians were more or less a Jewish sect. Paul who was free was perfectly free to take on Jewish vows or not. The Christians would often worship in the synagogues with the Jews, and it seems in Corinth, even after the leaders of the synagogue converted to Christianity they still oversaw Jewish worship. But also during this time hostilities escalated between Jews and Christians, and it was normally the Jews persecuting Christians. But this period of transition comes to an end with the destruction of the Temple in Jerusalem in 70 Ad. Christians took this as a sign that God would no longer consider such worship to be a valid form of devotion. Now, because they reject Christ as the Messiah, and refuse to see him as God, we cannot acknowledge that they worship God, but now it is they who worship God contrary to the law.