Note that caveat above: "in the West." Burrow admits right up front that he only tackles Western history, since otherwise he would be speaking (writing) out of his element. I don't blame him for that. If you've spent your entire career specializing in European history, attempting a layman's explanation of African or Asian history is not going to end well. It does make me wish for an equivalent book in those fields and on those subjects; I'll have to nose around Amazon to see what's out there.
The picture Burrow paints is not one of history as such, but rather of the people writing history. In other words, you're not going to learn all of the history you should have learned in high school (or forgot from high school) (guilty). If you want that out of the book, you should probably consult one of the many texts Burrow lists at the end of the book, which includes all of the works he discusses and many that he doesn't. They're all conveniently categorized by era and topic, so if there's a time period in particular you're curious about it's easy to find. I love books that recommend more books!
That said, in a way A History of Histories can still function as a good European history primer. Because it's about historians and historical texts, out of necessity Burrow has to take a very generalized, big picture view of trends and events. I can see how many people would find that kind of framing helpful before diving into more specific, specialized areas.
It's still heavy lifting, though. Burrow's writing, while totally lucid, is also incredibly dense and intricate, which makes skimming difficult. He was also English and (naturally) the book lingers a lot on all of the English history Americans like myself never properly learn in school (in favor of endless iterations of The Federalist Papers and The Stamp Act and The Civil War). Not a problem if you're English or familiar with English history; not even a problem if you're not, except that those sections of the book will deal with events and figures not intuitively familiar to you.
Maybe not a light-hearted beach read, but it's perfect for those of you who are still snowed in!