Summary: Living in accord with God's commandments not mans rules.
"You are the salt of the earth; but if the salt loses its flavor, how shall it be seasoned? It is then good for nothing but to be thrown out and trampled underfoot by men. "You are the light of the world. A city that is set on a hill cannot be hidden. Nor do they light a lamp and put it under a basket, but on a lampstand, and it gives light to all who are in the house. Let your light so shine before men, that they may see your good works and glorify your Father in heaven. "Do not think that I came to destroy the Law or the Prophets. I did not come to destroy but to fulfill. For assuredly, I say to you, till heaven and earth pass away, one jot or one tittle will by no means pass from the law till all is fulfilled. Whoever therefore breaks one of the least of these commandments, and teaches men so, shall be called least in the kingdom of heaven; but whoever does and teaches them, he shall be called great in the kingdom of heaven. For I say to you, that unless your righteousness exceeds the righteousness of the scribes and Pharisees, you will by no means enter the kingdom of heaven. (Mat 5:13-20 NKJV)
This passage follows the Beatitudes and is commonly known as the Sermon on the Mount. Jesus tells the Disciples that they are the salt that should flavor the souls of the people around them, that they are the light to lead people into the truth of the gospel. Then he says something that doesn't seem to fit with what has gone before. "I didn't come to set them aside (the law and the prophets)." No, I came to fulfill them to make them come true in my life. If you are going to be salt and light, you too must live by the true law and the words of the prophets, not by earthly rules and laws. He is saying that the law, which God had given to Moses on Mt. Sinai, was still in effect, that those who profess him as Lord need to also live by that law, and be more righteous than even the scribes and pharisees.
How do we live our lives with a greater degree of righteousness than even the Scribes and the Pharisees of Jesus' day? Well for one thing we need to look at how we justify not living in that manner. One of the favorite sayings of so many Christians is, "I'm not under the law, I'm under grace."
In that way we negate the law, we make it of no account because we are "under grace."
Then of course, when someone says something about our actions, we have the fall back position: "Don't judge me, you know what the Bible says about judging." Of course there is this from Matthew's gospel: Matthew 18:15 "If your brother sins against you, go and tell him his fault, between you and him alone. If he listens to you, you have gained your brother. But if he does not listen, take one or two others along with you, that every charge may be established by the evidence of two or three witnesses. If he refuses to listen to them, tell it to the church. And if he refuses to listen even to the church, let him be to you as a Gentile and a tax collector. Truly, I say to you, whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven." (Mat 18:15-18 ESV).
Now of course, there are those who will tell you that this language could not be Jesus, it had to be some priest later on who added these things to the Bible. But Jesus/God was the author of the law, for it was He who gave the law to Moses in the first place. Jesus indeed then, had come not to abolish the law but to establish it by His own life. Jesus lived as those around Him lived, only without sin. That was what He expected from those who would follow Him and teach others about the gospel. Now, let us take a look again at why Jesus was executed. According to the High Priest it was because he did not follow the law. He didn't wash his hands in the prescribed manner, he worked on the Sabbath by healing people, and of course Jesus claimed to be God. But, were these things in the Law that God handed down on Mt. Sinai? No, these were man made laws that were superimposed over the Law of God.
The law and the prophets, what we know today as the Old Testament, was what Jesus was speaking about, but there was also the Scribal or Oral tradition, and this is what Jesus spoke against for it was mans law not God's law.