"Whatever the future of historical studies, there should be no return to literal-mindedness."
Burke's book attempts to work out the narrative of "cultural history," it's revitalization towards the end of the 20h century, and it's future. Burke points to Burckhardt and Huizinga as the central early figures in the discipline and traces the rise of "New Cultural History" (NCH) as it took over from the 1970s.
So, what is cultural history? There is no clear-cut definition. It can only be defined in what unites its disparate scholarly manifestations: a sensitivity to "culture" (however that may be defined) as a crucial element in the interpretation of a historical moment. Unlike social historians, the cultural historian does not consider, dogmatically, the role of class and economics (the base of our base-superstructure) as the end all be all of historical reality. Instead, attention is paid to that very superstructure, elements of "culture" which provide evidence for any number of conclusions: mentalities, sentiments, social structures, etc.
What Burke does well appears in the concluding chapters. He is correct to point out the potential wholes in this methodological approach, and the potential future it faces in academia (including its increasing fusion with social history, or its rejection by empiricists/positivists). Burke, in his analysis of cultural history, wishes to point to the good: the ability of the discipline to look to marginal aspects of history and present them as new evidence for radical interpretations. This is an open-ended book, historiographic, but oriented towards a murky future.