The Pharisees and Herodians had very different political agendas, but there was one person that was a threat to both groups.  So they allied themselves “to entangle Jesus in His words” (Matthew 22:15–21).  It was a political trap.  It was about improper allegiance to an earthly ruler over the rightful kingship of God.  Jesus knew the malice of this trap, in spite of their flattery.  The wording of the coin itself was a statement to the Lordship of Caesar; that is why Jesus used it as an object lesson.  Jesus is Lord and not Caesar.  Give Caesar tax but not the allegiance that belongs to the One over the Kingdom of God.  There is always another lord competing with Jesus being King of your life.

Matthew 22:20–21 (ESV)  20 And Jesus said to them, “Whose likeness and inscription is this?” 21 They said, “Caesar’s.” Then he said to them, “Therefore render to Caesar the things that are Caesar’s, and to God the things that are God’s.”