the Herodians: partisans, courtiers, and clients of the Herod family who backed its rule
This is a group name, and it works like a nickname more than a formal title. The ending was borrowed from Latin, the same ending Romans used to label the people who belonged to or sided with a powerful man (Caesar's people, Pompey's people, and later Christ's people, the Christians). So the word simply means "the Herod side": the officials, retainers, soldiers, and well-placed supporters whose fortunes rose and fell with the ruling family.
The word never names a religious sect with its own beliefs, the way Pharisees and Sadducees do. It names a political circle. That is why it can cover a loose range of people, from courtiers around Herod Antipas in Galilee to the powerful priestly families in Jerusalem whom the dynasty had installed. What holds them together is loyalty to Herodian power, not a shared doctrine.
All three times the word appears, the Herodians are working against Jesus, and twice they are teamed up with the Pharisees, their natural opponents. The alliance is startling on purpose: religious traditionalists and political operators join forces because each sees the same threat. That the Herodians could supply real political muscle is the clearest clue to who they were, a group with genuine clout close to power, not a withdrawn or fringe movement.