Then they asked him a loaded question, "Is it lawful to pay taxes to the emperor or not?" If Jesus says it's all right to pay taxes to the Roman government, then he will lose face with most of his audience. For the Jewish community it was offensive to pay taxes to the hated Romans. Paying taxes was simply a way of supporting the Roman's detestable occupation. On the other hand if Jesus says it's wrong to pay taxes, then he will be in trouble with the Romans. It was a no win situation.
Jesus knew the Pharisees were trying to trap him. Fortunately he was wiser than they. He asks, "Show me the coin used for the tax." Jesus is using a subtle strategy here. One Pharisees produced a Roman coin from his pocket. Little did the Pharisee realize that in even possessing a Roman coin he already was well on the way to losing the argument. The Jewish people found the inscription on the Roman coins offensive, "Tiberius Caesar, Son of the Divine Augustus, Pontifex Maximus." To the Jewish people the inscription on the Roman coin was a deliberate break with the Ten Commandments that prohibit "graven images." For these and other reasons the Jewish people did not use Roman coins. They had their own temple currency. In producing a Roman coin the Pharisee showed which side he was really on.
Where we spend our resources says which side we are really on too.