“Anyone who divorces his wife and marries another woman commits adultery, and the man who marries a divorced woman commits adultery.”
The NIV titles this section "additional teachings". It almost seems a hodgepodge of ideas that do not flow with the rest of the passage. But since that isn't Jesus' style, let's take a closer look. Why are these verses sandwiched between the story of proper use of money and the parable of the rich man and Lazarus? Taken all together, Jesus is pointing the finger at the false religion of the Pharisees and pointing out the dangers within the system.
Again and again Jesus points out that a person's outward religiosity is no indication that the person is part of the kingdom of God. He called the most religious people in the land "whitewashed tombs" - clean on the outside but inside filled with rotting decay.
The Law and the Prophets are what Christians today call the Old Testament. Until the coming of John the Baptist, these scriptures proclaimed the truths of God and revealed man's inability to live up to a perfect holy standard. The arrival of John and Jesus marked the beginning of a new era. The "sinners and tax collectors" had been held at arms length from God by these Pharisees. Now they were forcing their way in droves through the open door of the gospel.
Jesus came to fulfill the Law, not destroy it. Not even a mark the size of a period or dash will be removed from the Law until heaven and earth pass away. Some of the sacrificial laws and cultural laws are not followed by Christians, but the meaning of the law as taught by Jesus certainly is. Although he interacted with and offered grace to those considered sinners by society, he set the standard for righteousness even beyond the law in teachings such as the Sermon on the Mount. "You think you're righteous because you haven't murdered? If you've hated anyone it is the same thing. You think you're sinless because you haven't committed adultery? If you've lusted you are equally guilty under the Law." He lived a sinless life and imputes that righteousness to all who believe.
Verse 18 seems totally out of flow, almost like a random thought. But he was calling out the Pharisees who had married divorced women or been divorced themselves. They would never have sex outside the bonds of marriage, but in the eyes of the Law divorce and remarriage was equivalent to adultery. They wanted to pick and choose which sins were allowed and which were grievous.
Don't we all. Some sins - sexual sins, divorce, murder, rape, child abuse - are seen by many Christians as worse than others - gossip, white lies, mildly lustful feelings, jealousy, overindulgence. We like to justify ourselves by pointing the finger at others. We condemn Gosnell and the Tsarnaev brothers to hell but give ourselves a free pass. Of course some sins have greater repercussions on earth. Of course our human laws should punish some sins greatly and ignore others. But in the eyes of a holy God, sin is sin. "For whoever keeps the whole law but fails in one point has become accountable for all of it" (Js 2:10).
So now turn from your conscience and its feeling to Christ who is not able to deceive; my heart and Satan, however, who will drive me to sin are liars... You should not believe your conscience and your feelings more than the word which the Lord who receives sinners preaches to you... Therefore you are able to fight with your conscience by saying: You lie; Christ speaks the truth and you do not. - Martin Luther