What does Matthew 14:3 mean?

The last time Matthew wrote about John the Baptist, he explained how John sent a message to Jesus from Herod's prison (Matthew 11:2–6). To begin this passage, Matthew looks back to explain how John the Baptist got there. In short, John was publicly criticizing Herod Antipas for unlawfully marrying his half-brother Philip's former wife, Herodias. She seems to have taken great exception to this, manipulating her husband more than once to act against John (Mark 6:14–29). At first, Herod arrested, bound, and imprisoned John for the sake of Herodias' anger.

Herod Antipas, called Herod the tetrarch here, was one of the sons of Herod the Great, who had ordered the death of the babies in Bethlehem shortly before his own death (Matthew 2:7, 13). Herod Philip was another of Herod the Great's sons. Herod Antipas divorced his own wife and Herodias divorced Philip so the two could get married. Herod was Jewish, though, and Jewish law forbade marrying the wife of one's brother while he was still living.

Herod likely imprisoned John at his hilltop fortress known as Machaerus, east of the Dead Sea.