A dominant discourse is just what it sounds like it is. It is the way of thinking and talking that convinces nearly everyone in a culture. Just as I might get mad if you kissed me when I was asking for a cookie, so tempers flare when this confusion between dominant discourse and metanarrative leads people into disputes. A metanarrative is not a dominant discourse, at least not necessarily. Today, astrology is not a dominant discourse.
Science is dominant.
Still, there are a circle of people today who believe in astrology and they believe in a metanarrative. In the last week I looked over some notes of people arguing about postmodernism. Postmodernism is this other thing. But when I looked carefully at these notes, I think I see this mischievous differend smiling back at me. The dominant discourse is what most people believe.