Supporters of Herod's dynasty, and therefore of Rome — which is why finding them agreeing with the Pharisees is the signal.
The Herodians are a political faction rather than a religious one: backers of the Herodian house and the Roman arrangement that kept it in place. They appear only a few times, and always allied with the Pharisees, who on every other question were their opposites. That is the point of mentioning them. When Mark says the Pharisees took counsel with the Herodians about how to destroy him, the alliance itself is the news.