Summary: Jesus says, "Render to Caesar the things that are Caesar's; and to God the things that are God's" (Matt 22:21). Most sermons on this verse deal with the first part of this verse, but what does the second part mean? What does it mean to render to God?
The Jews were desperately seeking to discredit Jesus, because within the context, He was speaking parables against them. They would stop at nothing to do so. Within the context of this verse, various groups ask Him questions designed to trap Him or challenge Him. These questions, when answered, show the hearts of those who asked them. Jesus shows what they are lacking in their "service" to God.
Matt 22:23-33: The Sadducees ask about the resurrection (which they didn't believe in). They think up some kind if hypothetical situation that they believed was rock solid in proving that it was incorrect to believe in the resurrection. Jesus quickly answers their question, showing how they have ignored Old Testament texts which answered the question. They were not digging deep enough in their studies of scripture
Matt 22:34-39: One of the Pharisees, a lawyer/scribe, to test Jesus, asked Him what the most important commandment of the law is. Jesus' answer shows the hypocrisy of the Pharisees and how they were neglecting the most important things about serving God. Jesus tells them to love the Lord God with all their soul, mind, & strength was the most important commandment (which was a commandment they were clearly violating in scripture) and the second commandment He gives without being asked, to love your neighbor as yourselves, which they were also violating in trying to test and discredit Jesus so they would have reason to kill Him.
Matt 22:15-22: But before these things, they ask a very challenging question of Jesus about paying taxes to Caesar which He also answers with great wisdom:
"Then the Pharisees went and plotted together how they might trap Him in what He said. 16 And they sent their disciples to Him, along with the Herodians, saying, "Teacher, we know that You are truthful and teach the way of God in truth, and defer to no one; for You are not partial to any. 17 "Tell us then, what do You think? Is it lawful to give a poll-tax to Caesar, or not?" 18 But Jesus perceived their malice , and said, "Why are you testing Me, you hypocrites? 19 "Show Me the coin used for the poll-tax." And they brought Him a denarius . 20 And He said to them, "Whose likeness and inscription is this?" 21 They said to Him, "Caesar's." Then He said to them, "Then render to Caesar the things that are Caesar's; and to God the things that are God's." 22 And hearing this, they were amazed, and leaving Him, they went away."
They set up this question in an interesting way. They characterize Jesus as One who is not a respecter of persons. He is not "swayed by appearances," or as it literally means "you do not look into the face of men." This may be a reference to Leviticus 19:15 which says :
“You shall do no unrighteousness in judgment: you shall not respect [receive, cp. Luke 20:20] the person [“face” in Hebrew and LXX] of the poor, nor honor the person [face] of the mighty: but in righteousness shall you judge your neighbor.”
They are in a sense telling Jesus that they believe that He does observe this passage. He is not a respecter of persons. Most commentators seem to think the leaders’ approach to Jesus is mere flattery. This may or may not be true; Either way, they were trying to trap Him with God’s Word. They were, in other words, saying, “You truly serve God only and only make judgments based on truth, not on the status of man. Therefore, is it right to give tribute to Caesar?”
They asked about paying taxes. The specific tax in question was the “poll tax” or “head tax” which was based on a census of the people and had to be paid on all persons including women and slaves. It was charged every person because of the services that the state gave the people. And by law it had to be paid by means of Roman coinage.
So Jesus seems to be in a bind. If Jesus said “No” He could be in trouble with the Roman authorities for encouraging tax evasion and treason against Caesar. This seems to be the answer that the Jews and Herodians desired, because they were seeking a reason to trap Him "so that they could deliver Him to the rule and the authority of the governor" (Luke 20:20). If Jesus said “Yes” He would certainly lose the support of the people who saw Him as a Messiah against Roman occupation. Either way, the Pharisees and Herodians would win. They had a way that they could discredit Jesus.
Jesus didn't answer the question at first. Jesus responded immediately by calling them hypocrites. He who knows the hearts of men (since He is God) knew the motives behind them asking the question. Their motives showed that they didn't want the "truth." They were more concerned with themselves, their influence, and getting Jesus (who was hurting their influence) out of the way.