The Jews had tried many times to accuse Jesus on the basis of religious issues and had always failed. Now they approached Him about paying taxes in hopes that His answer might give them the opportunity to deliver Him to Pilate for prosecution.
These Pharisees and Herodians reasoned that any answer that Jesus gave would be wrong. If He approved of the Roman taxes, then He would lose popularity with the masses. If He spoke against the Roman taxes, then the Jews would hand Him over to the Roman government and Pilate would dispose of Him. It looked like they had Jesus trapped. Jesus, however, answered with such simple wisdom that these Pharisees and Herodians were caught in their own trap and made to look like fools.
Jesus declared, "Render [give back] to Caesar the things that are Caesar's, and to God the things that are God's" (Mark. 12:17). People are made in God's image, so we must render to God the things belonging to God [our lives] and to Caesar the things belonging to Caesar [his money and other benefits of his rule].