Acts 18 So Paul still remained [e]a good while. Then he took leave of the brethren and sailed for Syria, and Priscilla and Aquila were with him. He had his hair cut off at Cenchrea, for he had taken a vow. 19 And he came to Ephesus, and left them there; but he himself entered the synagogue and reasoned with the Jews.

The vow Paul took was the Nazarite vow. This vow was intended to show Jews that Paul still respected the law.
I had to hit up Wikipedia to find out what the Nazarite vow was:
1. Abstain from wine, wine vinegar, grapes, raisins, intoxicating liquors, vinegar made from such substances, and eating or drinking any substance that contains any trace of grapes.
2. Refrain from cutting the hair on one’s head; but to allow the locks of the head’s hair to grow.
3. Not to become ritually impure by contact with corpses or graves, even those of family members.

People debate whether he was finishing the vow, or had just started, but whatever…
Now Paul is entering the synagogue to do what he does; reason with the Jews.