What does Matthew 14:8 mean?

Herodias had reason to hate John the Baptist. John had publicly called out Herod Antipas as a lawbreaker for marrying her, since Herodias had previously been married to Herod's brother Philip. That criticism called her morals into question, as well, so it's not surprising she took John's declarations personally. Probably at her direct request, Herod has already arrested and imprisoned John inside his fortress (Mark 6:17). He would not go so far as to kill John the Baptist, however, because of his duty to keep the peace in his part of Israel. Many people in Israel believed John was a prophet sent from God.

Now, though, Herodias seizes an opportunity to have her ultimate revenge against John for declaring her sin to the world. Herod has made an impulsive and likely drunken promise to Herodias' daughter. This is her child by Antipas' brother, her former husband. Herod was so pleased with the girl's birthday dance for him and his guests that he has promised to give her anything she asks.

Herodias tells the girl exactly what to ask Herod for: the head of John the Baptist on a platter. She puts the gruesome request in the mouth of the girl, forcing Herod to either dishonor himself before his guests or have John executed and risk the disfavor of the people.