Righteousness is being accepted before Almighty God; it is the state being found before the presence of Almighty God without the sense of unworthiness or condemnation.
Righteousness can never be accomplished through the merits of what a man can achieve in his own power or effort, but only on the acceptance of all that Jesus Christ has accomplished on behalf of mankind.
A believer can stand before our Heavenly Father through being in Jesus Christ, who has taken our unrighteousness and given to us His right-standing with His Father, when the Father sees a believer He accepts them not in the power of anything they have done, but because of all that Jesus Christ has accomplished in His work of Salvation.
For I say to you that unless your righteousness shall abound above that of the scribes and Pharisees, you shall never enter into the kingdom of the heavens. Matthew 5 v 20
But seek first the kingdom of God and His righteousness, and all these things will be added unto you. Matthew 6 v 33.