Broken Balls: When Fortunes Turn Foul is a book about Divination. It is a book that is supplied by the teacher Of Divination instead of the pupil having to purchase it due to the high cost of over 15 Galleons. It is one of the few books on Divination that Hermione Granger had read before she was 'insulted' by Sybill Trelawney. Trelawney is rather fond of using this book in lessons to 'open the minds' of her students.
An interesting sidenote is that, in the world of sex the name of the book, Broken Balls: When Fortunes Turn Foul can be intended to have a double-edged meaning, because a lack of testicles can change the fortunes of a man, often for the worse.