Unless your righteousness exceeds the righteousness of the scribes and Pharisees My question is based on Matthew 5: 17-20

This question addresses the first part of the passage. The second part is the phrase


  Unless your righteousness exceeds the righteousness of the scribes and
  Pharisees, you will by no means enter the kingdom of heaven. -- verse 20 - emphasis mine.


What does Jesus mean by "unless your righteousness exceeds the righteousness of the scribes and Pharisees"? Any help to make me understand this important passage will be much appreciated.
The Scribes and the Pharisees were the religious leaders. They were role models for the people to follow. They were blameless in their religious observances. The people looked at them for guidance. The people must have believed that the Scribes and the Pharisees were the first to enter the kingdom of Heaven. However, Jesus was teaching them that God's standard is higher than what man can accomplish. From  Matthew 5:21 onward, we clearly see the standard of God for anyone to be counted as perfect. For instance, while the Pharisees never slept with another woman, Jesus was telling them that even a lustful gaze is already an adultery.

We cannot enter heaven with our works and observance to the law, for we can never meet the standard required by God. We need God to save us. Therefore, God gave us His one and only Son, Jesus Christ, a perfect person to take our place and help us reach the standard demanded by God. For Jesus said "No one comes to the Father except through me" (John 14:6).

This is clearly explained by Paul in his Epistle to the Romans.


  Romans 3 (NIV)
  
  [10] As it is written: “There is no one righteous, not even one;
  
  [20-31] Therefore no one will be declared righteous in God’s sight
  by the works of the law; rather, through the law we become conscious
  of our sin. But now apart from the law the righteousness of God has
  been made known, to which the Law and the Prophets testify. This
  righteousness is given through faith in Jesus Christ to all who believe. There is no difference between Jew and Gentile, for all
  have sinned and fall short of the glory of God, and all are
  justified freely by his grace through the redemption that came by
  Christ Jesus. God presented Christ as a sacrifice of atonement,
  through the shedding of his blood—to be received by faith. He did this
  to demonstrate his righteousness, because in his forbearance he had
  left the sins committed beforehand unpunished— he did it to
  demonstrate his righteousness at the present time, so as to be just
  and the one who justifies those who have faith in Jesus. Where, then,
  is boasting? It is excluded. Because of what law? The law that
  requires works? No, because of the law that requires faith. For we
  maintain that a person is justified by faith apart from the works of
  the law. Or is God the God of Jews only? Is he not the God of
  Gentiles too? Yes, of Gentiles too, since there is only one God, who
  will justify the circumcised by faith and the uncircumcised through
  that same faith. Do we, then, nullify the law by this faith? Not at
  all! Rather, we uphold the law.