Righteousness is the Old English word for “right standing”.
In the simplest terms, it is just means doing the right thing.
That’s it. That’s what it means.
If I ask you what 2+2 is and you answer “4”, you are mathematically righteous, or right.
God calls you to be righteous, or right, according to His standard. And you are to be right all the time, and not right in your own eyes (self-righteous) because you don’t have all the facts.
Since God is always right, incapable of error, following His lead on, well, everything, is a grand idea.