Jameson is a Marxist Political Theorist (which is actually a school of philosophy, not just politics). He wrote this book as an elaboration on an article by the same title which was received as controversial.
He begins by outlining a basic Hegelian dialectic model, where a status quo (thesis) is confronted by a new competitive idea (antithesis) for the formation of an adapted status quo (synthesis). This is the basic outline that led Engels and Marx to publish "The Communist Manifesto," so Jameson applies this basic model of analysis to Postmodernism and Capitalism.
He returns to the issue of narrative. The Modernists argued that humans operated on essential narratives, like myths, which unite us, but Postmodernism brought the rejection of "meta-narratives." A meta-narrative is a theoretical abstraction from a real story (for the purposes of interpretation typically, since analyzing the structure of a narrative can help show what the story "means"). Jameson argues that Postmodernism represents the culture's new awareness of meta-narratives, their resultant skepticism, and the rise of irony and detachment in Western art.
Then he turns to culture to show that the effect of Postmodern ideology is the rejection of truth-claims. Whenever someone says they know the truth, our Postmodern society would reject the truth-claim without entertaining it.
This led to the rise of what Jameson calls "corporate capitalism," as businesses tried to navigate a new market. He mentions the Austrian school (especially Adorno, who wrote the authoritative book on Postmodernism and media, "Dialectic of Enlightenment," an important book about society and the value of art in human enlightenment). He agrees that in film, literature, architecture, and visual arts, the combination of Postmodernism with Capitalism did lead to the elimination of meaningful art from the culture.