What does Matthew 14:6 mean?

Ancient Jewish people, so far as we know, invested little importance in annual birthdays. Celebrating the date of one's birth, as is done in most modern cultures, was not common among Israelites of the New Testament era. The historian Josephus wrote—possibly exaggerating—that the practice was forbidden. The Jewish family of the Herods, however, was greatly influenced by Greek culture in many ways, including this one. Herod threw himself a lavish birthday party, likely at his fortress called Machaerus, found on the east side of the Dead Sea.

The Herod mentioned here is Herod Antipas, also known as Herod the tetrarch. His current wife, Herodias, had a daughter by her previous marriage—to Herod's own brother Philip, known as Herod II. We know from history that the daughter's name was Salome. Salome was likely a teenager at this time. She performed a dance for Herod and those gathered to celebrate his birthday. Some commentators suggest that this dance may have been very sensual, given the time and the setting, as well as the reaction (Matthew 14:7; Mark 6:22–23). However, Matthew's gospel does not say this directly.