Lords - Μεγιστασιν, probably governors of particular districts.
High captains - Χιλιαρχοις; literally, chiefs or captains over a thousand men, military chiefs.
Chief estates - Πρωτοις; probably such as might be called nobles by title only, having no office civil or military; probably magistrates. See Kypke an the place.

And when a convenient day was come,.... For Herodias; who had long sought and watched for an opportunity of avenging herself on John, and such a time Herod's birthday proved; though some think, that this phrase is the same with , "a good day"; often used by the Jews for a festival, any one of their feast days; there is a tract in their Misna which bears this name; and that such a day was this. But not one of the festivals of the Jews was this, as either their passover, or pentecost, or feast of tabernacles, which Herod had no regard to; but his own birthday, which he kept as a festival, in eating, and drinking, and dancing; and so was a very opportune and seasonable time for Herodias to take the advantage of Herod when in a good humour, amidst his company, and in his cups, to solicit that, which she had often done without success: and so it was now,
that Herod on his birthday made a supper to his lords, high captains, and chief estates of Galilee: this birthday, was either the day of his natural, or civil birth; the day when he was born into the world, or of his accession to the throne; See Gill on Matthew 14:6, when he made a grand entertainment in the evening for his nobles, and the officers of the army, the captains of thousands, and the principal men, those of the first rank and quality in Galilee, of which he was Tetrarch.

And when a convenient day--for the purposes of Herodias.
was come, that Herod--rather, "A convenient day being come," when Herod.
on his birthday, made a supper to his lords, high captains, and chief estates of Galilee--This graphic minuteness of detail adds much to the interest of the tragic narrative.

When a convenient day was come. For the execution of the plans of the vengeful woman.

A convenient day - Convenient for her purpose. His lords, captains, and principal men of Galilee - The great men of the court, the army, and the province.