There are many theological words which most people — even most Christian people — do not under-stand. Among these is the Bible word “righteousness”. Actually, though, this word is very simple and we ought to understand about God’s righteousness even before we learn of His love.
Righteousness is simply an old word for rightness. When we say that God is righteous, we simply mean that what He does is always right; that He will not and cannot do anything that is not right. This is why Paul declares in Romans 1:16, 17:
“I am not ashamed of the gospel of Christ, for it is the power of God unto salvation to every one that believeth…FOR THEREIN IS THE RIGHTEOUSNESS [rightness] OF GOD REVEALED…”
We are proud to proclaim the gospel of the grace of God because it emphasizes God’s rightness. The gospel does not tell us that God will overlook our sins or wink at them and smuggle us into heaven. It doesn’t tell us that He will forgive us if we are sorry enough or do enough good deeds to counterbalance our sins. By no means.
The “gospel of the grace of God” is based on His rightness. It is the wonderful message that “Christ died for our sins”, that He paid for them Himself so that He might justly offer us forgiveness and declare us righteous.
Romans 3:26 puts it beautifully. There the apostle declares that since our sins were paid for by Christ at Calvary, God can now “be just — and the Justifier of him who believes in Jesus”.
For centuries religious people have said to each other: “We must be truly sorry for our sins and do all the good we can and surely God will forgive and accept us”. But this is not the gospel. The gospel gives us more solid ground to plant our feet upon. It says to every man, woman and child: “Your sins were PAID FOR by Christ at Calvary. Trust in Him and you will be saved”. This is gospel [good news] indeed, for it is based on the just payment of the penalty for sin. source