Romans 10:3: For, Being Ignorant Of The Righteousness Of God, And Seeking To Establish Their Own, They Did Not Submit To God's Righteousness.
 For, being ignorant of the righteousness of God, and seeking to establish their own, they did not submit to God's righteousness. (ESV)
There is within each one of us a desire to be righteous. Even those who claim to not believe in God at all will hold out some sort of standard that they expect people to live up to. It was this very reality that led the great C. S. Lewis to a belief in God. He knew that certain things were unjust, or unrighteous, and that led him to the pursuit of the source of that standard of righteousness.
Paul is speaking in this verse about Jews who were ignorant of the righteousness of God. This is beyond tragic. The Jews were the recipients of the very Law of God. They were given the Scriptures which were the written revelation of God himself. If any group of people should have known the righteousness of God it would have been the Jews.
The Jews looked at all of the Law and missed the whole point of it. Instead of the Law leading them to a humble recognition of their own sinfulness, they concocted their own efforts to be righteous based on their own works. They even emphasized some of their own traditions as having equal weight as God's Law. They held themselves to their own standards, not God's.
There is a danger here. We could look at the Jews' response to the Law and criticize them. Yet, all of mankind falls into the same trap. When we look at God's righteous standard and decide that we would rather live by our own standards of righteousness we are no different than the Jews. If we are not willing to submit to God's righteousness we will end up establishing our own.
Only yielding to God's righteous standard will lead to a right relationship to God. Put aside any effort to establish your own idea of righteousness. Submit to the Lord. Repent of your sin. Receive the forgiveness that Christ paid for. He will give you God's righteousness as a free gift.