What are the things that belong to God?

Then the Pharisees went out and conspired to trap Jesus in His words. They sent their disciples to Him along with the Herodians. “Teacher,” they said, “we know that You are honest and that You teach the way of God in accordance with the truth. You seek favour from no one, because You pay no attention to external appearance. So tell us what You think: Is it lawful to pay taxes to Caesar or not?”   

But Jesus knew their evil intent and said, "You hypocrites, why are you testing me? Show Me the coin used for the tax.” And they brought Him a denarius.

"Whose image is this," He asked, "and whose inscription?" 

“Caesar’s,” they answered. So Jesus told them, “Give to Caesar what is Caesar’s, and to God what is God’s.” Matthew 22:15-21

The Pharisees were learned people of the Law and knew how to trap Jesus. Had He said "Yes ... pay taxes to Caesar," they would have accused Him of siding with the occupying Roman Empire and was thus the enemy of the Jews. The Herodians, who were loyal to Herod, the Jewish King, would have reported Him to their King as a traitor.  

But if Jesus said don't pay taxes, He would have been seen as opposing Caesar and His occupying forces. 

So what does Jesus' answer, "Give to Caesar what is Caesar’s, and to God what is God’s.” mean?

Let us consider all the gifts that God has bestowed upon us. Our health, our families, our talents, strength, abilities and so on. None of us is where we are in life without God's love, generosity, mercy and gifts.

Whatever our talents ... skills at doing difficult intricate work like science, medicine and so on, talents in music, the arts, sports or whatever ... anything we are able to do is the result of God's gifts to us. We did not make ourselves clever at learning, inventing, creating or whatever we can do in life.

These are the things that are God's. 

We should use our skills, talents or whatever we are able to do in life for the betterment of others less fortunate than ourselves. 

"Love one another as I have loved you". Use your gifts for the glory of God.