The name ‘Herodias’ is a transliteration from the Greek Ἡρῳδιάς (hērōdias). It is the feminine form of the male name Herod which is Ἡρῴδης (hērōdēs) in Greek.
Herodias was a granddaughter of King Herod the Great and she lived from about the year 15 BC to about 39 AD.
The marriage that John the Baptist criticized was the union between Herodias and Herod Antipas, who was tetrarch of Galilee and Peraea. He also was one of her uncles. Her marriage to Antipas violated Jewish law because she was already married to another man who was still living. That other man was Herod Philip, who also was an uncle of hers, and a brother to Antipas.
Herodias had been married previously to yet another uncle, Herod II, but he had been assassinated. Through Herod II, Herodias had a daughter named Salome. During a party that Antipas was hosting, the daughter danced for him and his guests. Antipas was so pleased with her dance that he pledged to give her anything she requested. She then went to her mother, Herodias, and asked her what she should request, and Herodias told her to ask for the head of John the Baptist.
Although Antipas did not want to kill John the Baptist, because he feared that it would anger too many people, he consented to the request because he had given his word to Herodias' daughter in front of his party guests. A short time later, the head of John the Baptist was set on a platter and delivered to Herodias and her daughter.
In 39 AD, Antipas began stockpiling weapons to make war on King Aretas IV of Nabatea. Antipas's brother Herod Philip (Herodias's first husband) reported the weapons stockpile to Emperor Caligula (reigned 37-41 AD) who was known for his paranoia and megalomania. Fearing Philips's intentions, Antipas and Herodias went to Rome to defend themselves before Caligula. But the letter from Herod Philip got there first. Caligula had Antipas stripped of his tetrarchy and exiled to Gaul. Caligula allowed Herodias the option of going back to Herod Philip who was now given Antipas's kingdom. But Herodias refused and joined her husband in exile. All we know is that Antipas and Herodias lived out their days in exile in Gaul and they never saw Judea again.