The gospel is the salvation for everyone who believes (1:16), and this salvation is received by faith alone, not by works (1:17).  

Again, salvation is:
1.  for everyone who believes
2.  received by faith alone, not by works

Paul explains that this gospel reveals God’s righteousness.  A part of what it means that he is righteous is in how he gives an opportunity for humanity to receive that righteousness.  

This “gospel” is the fact that:
1. God is righteous
2. All people are unrighteous
3. Christ’s life, death and resurrection imparts righteousness on all people who believe 

Incidentally, I would add these truths:
4. All who accept this by faith are declared righteous
5. God's provision of this affirms his righteousness
6. The gospel, therefore, reveals God's righteousness (in more than one way)

Thus, those who live by faith are made righteous and they truly live (1:17b).  It is the “power” of God because it is able to make you righteous, whereas nothing else can (not works).