John Lightfoot on Matthew 14:6

[And when Herod's birthday was kept.] The Jewish schools esteem the keeping of birthdays a part of idolatrous worship: perhaps they would pronounce more favourably and flatteringly of thine, O tetrarch, because thine.

These are the times of idolaters: the Kalends; the Saturnalia;...the birthday of the kingdom; and the day of a man's birth...

[The daughter of Herodias danced.] Not so much out of lightness, as according to the custom of the nation, namely, to express joy and to celebrate the day. The Jews were wont in their public and more than ordinary rejoicings, and also in some of their holy festivals, to express their cheerfulness by leaping and dancing. Omitting the examples which occur in the holy Bible, it is reported by the Fathers of the Traditions, that the chief part of the mirth in the feast of Tabernacles consisted in such kind of dancing: the chief men, the aged, and the most religious, dancing in the Court of the Women; and by how much the more vehemently they did it, so much the more commendable it was. The gesture, therefore, or motion of the girl that danced took not so much with Herod, as her mind and affection: namely, because hereby she shewed honour towards his birthday, and love and respect towards him, and joy for his life and health: from whom, indeed, Herod had little deserved such things, since he had deprived her father Philip of his wife, and defiled her mother with unlawful wedlock and continual incest.