This post will serve as a part of a glossary for future posts.
"Works Righteousness" is a term referring to the idea that one can earn the favor of God. This applies even to people who don't believe in God. In that case, it is the belief that good deeds will make the world a better place, or at least make one a better person.
It is my understanding that Christianity is the only belief system which does not emphasize works righteousness. That is, righteousness (literally right standing with God) is a free gift from God (formally referred to as grace). Works follow from (are the fruit of) grace.
The difference is outwardly subtle. Everyone wants to "do good". But the Christian realizes this does not make one "good". Everything good comes from God, and doing good is what is expected of us. There is no special reward for doing your job! (but there is pay)