Teacher, tell us what is your opinion, is it lawful to pay the census tax to Caesar or not?" (Mt 22, 15-21) To approve meant to be a traitor to his brothers and to be one with the Romans; to disapprove meant to work against the Romans and be subjected to an accusation of rebellion.
The answer was unexpected: "Then repay to Caesar what belongs to Caesar and to God what belongs to God." as a way of saying "you who receive a lot from the Romans, many things, pay for that to them in the same measure or don't receive it, and you who receive many things from God, return to Him in the same proportion"
An interesting shift in Jesus' answer could point us in the direction of the importance of the saying. The question was whether one should give (Greek didômi) tribute to Caesar. But Jesus' answer spoke of giving back, paying back (paradidômi), as if one already owed something (and notice that after Jesus is asking for the coin it is from their pocket from where the coin is coming). What Jesus said could be paraphrased as: "Give back to Caesar what is Caesar's due, and to God what is God's due." Instead of answering the direct question of whether one should pay the forced tribute to Caesar or not, Jesus raises the question to another level, that of the principle of justice. Greek philosophers before Jesus defined justice as "giving back to everyone what is their due." Jesus seems to be saying that the only binding obligation is that of justice, that of giving back to every person what is due to them. Serving God is basically a matter of justice? If God has given us all that we are and have, then we are bound in justice to give back to God great gratitude, great loyalty and exquisite service. The central act of Christian worship is called Eucharist, which means "thanksgiving." It is basically a question of paying back the debt of gratitude that we owe to God.
Then the question for us is how can I repay the Lord for all the great good He has done for me? I will raise the cup of salvation. Which means that I will offer Him all that I have. Jesus talked about the cup at least on two occasions referring to His Great Passion and Sacrifice on the cross: "Father, if you are willing, take this cup from me; yet not my will, but yours be done." (Lk 22, 42)... and when the two disciples came asking for the first places in the kingdom: Can you drink the cup I am going to drink? (Mt 22, 20)
The answer of what should we do to repay to God all that He has given us is: With all that we have my brothers and sisters.