But now the righteousness of God has been manifested apart from the law, although the Law and the Prophets bear witness to it— the righteousness of God through faith in Jesus Christ for all who believe. For there is no distinction: for all have sinned and fall short of the glory of God, and are justified by his grace as a gift, through the redemption that is in Christ Jesus, whom God put forward as a propitiation by his blood, to be received by faith. This was to show God’s righteousness, because in his divine forbearance he had passed over former sins. It was to show his righteousness at the present time, so that he might be just and the justifier of the one who has faith in Jesus.(Romans 3:21-26, ESV).
We all basically know what righteousness means. A good dictionary definition would be the quality of moral uprightness or justice, being virtuous, having no sin. But when you use righteousness in connection with God you have a totally different definition. To get an idea of what I am talking about, here is a brain teaser that I learned years ago:
The righteousness of God is that righteousness which His righteousness requires Him to require.
When you get your mind around that definition of righteousness then you realize that there must be punishment for sins, and there must be perfect righteousness for any one to be able to stand in the presence of God. That is why Jesus came and suffered for sinners like you and me.