Steven Pinker's main point in The Better Angels of Our Nature: Why Violence Has Declined is this:
The “Kantian triangle of democracy, open economies, and engagement in the international community” (310) is his main causal theory of the decline of violence. Each of these institutions justifies itself by the reasonable gains that people get from them, and from the spread of Enlightenment culture as a whole.
The spread of competent states with somewhat open economies has reduced violence because
a) violence by citizens is bad for states;
b) violence by the state against citizens is bad for states, unless it is necessary for a);
c) violence is bad for commerce;
d) interstate institutions have been somewhat successful in preventing interstate violence (wars).
The places that we see violence in the world today are in failed states, weak states, and relatively lawless corners of otherwise competent states. And these places are shrinking as states and globalized commerce fill the remaining lawless corners of the world.