In this case, Rowling has written bios of Dolores Umbridge, Horace Slughorn, Quirrel and Peeves the Poltergeist. They partly felt like a summary of events from the books, although there was some stuff that I didn't know - I can't confirm that it was new material, or just stuff I forgot from the books (for example, Umbridge's eventual fate). While it wasn't all that original, it did offer a fascinating insight into the characters that would be useful for newbies.
The only real problem then was that I'd expected new stories about adventures at Hogwarts, which isn't what this book was about, although JK Rowling did offer a fascinating insight into her thoughts about the characters, including how they got their names (Umbridge is inevitably a play on the term "to take umbrage").
There are also a few short explanations of other aspects of Hogwarts life, such as equipment used in potions class, and spells (along with some comments about how Hermione could use polyjuice potion at the age of 12).
The section of past Ministers of Magic could have sounded like a dramatis personae from one of George R.R. Martin's A Song of Ice and Fire novels, but I started to enjoy it, mostly because of Rowling's imagination, and the humour, particularly when she started including historical figures and events (for example, a Minister accused of fixing the 1966 World Cup final).
This is a good choice for anyone not that familiar with the Potter universe, but for diehard fans, there is very little in terms of new material.
Next book: Coot Club by Arthur Ransome