The Herodians derived their name as followers of King Herod. The Herodians were a political party that wanted to restore a Herod to the throne in Judea as well as other areas ruled by Herod the Great. They were political foes of the Pharisees who wished to restore the kingdom of David.

They Are Mentioned with the Pharisees

We only find them being mentioned three times in the gospels and always in conjunction with the Pharisees. Although politically opposed to the Pharisees they participated with them in the persecution of Jesus. After Jesus broke their interpretation of the Sabbath, they plotted to kill Him.

The Pharisees went out and began to plot with the Herodians how they might kill Jesus (Mar 3:6).

They also attempted to catch Jesus in saying something that could be used to arrest Him.

They [the Pharisees] sent their disciples to him along with the Herodians (Mat 22:16).

Jesus Warned of the Leaven, or the Yeast, of Herod

Jesus spoke of the leaven of Herod.

And he was giving orders to them, saying, "Watch out! Beware of the leaven of the Pharisees and the leaven of Herod" (Mar 8:15).

This may refer to Herod Antipas or the Herodians.

Summary

The Herodians were a political party who wanted to restore a Herod to the throne in Judea. They were opposed to the Pharisees who wanted a descendant of David on the throne. They joined with the Pharisees in attempting to silence Jesus.