The words should run thus: And when the daughter of Herodias herself came in καὶ εἰσελθούσης τῆς θυγατρὸς αὐτῆς τῆς ἡρωδιάδος. The intention of the evangelist is to point out that it was Herodias's own daughter who danced, and not a mere professional dancing-girl.
Josephus mentions that dancing-women were admitted to feasts by the Jews; and Xenophon testifies to the same custom amongst the Greeks.