"Luther was looking now at the Greek word that was in the New Testament, not the Latin word. The word dikaios, dikaiosune, which didn’t mean to make righteous, but rather to regard as righteous, to count as righteous, to declare as righteous.
And this was the moment of awakening for Luther. He said, 'You mean, here Paul is not talking about the righteousness by which God Himself is righteous, but a righteousness that God gives freely by His grace to people who don’t have righteousness of their own.'
And so Luther said, 'Woa, you mean the righteousness by which I will be saved, is not mine?' It’s what he called a justitia alienum, an alien righteousness; a righteousness that belongs properly to somebody else. It’s a righteousness that is extra nos, outside of us. Namely, the righteousness of Christ.
And Luther said, 'When I discovered that, I was born again of the Holy Ghost. And the doors of paradise swung open, and I walked through'."
Cited from R.C. Sproul – http://www.ligonier.org/blog/justification-faith-alone-martin-luther-and-romans-117/