First, I'll admit that I have not yet finished reading the entire Harry Potter series. I've stalled about a hundred pages into Goblet of Fire. So I have no context for the appearance of Beedle's stories somewhere in the later books or of Hermione's or Dumbledore's relation to them.
That said, I don't think much context is needed to read this book. Rowling does include elements from her magical world (references to "muggles" and different characters, books and places) but she also includes footnootes to many/most of these, so I suspect/hope that the virgin Rowling reading would be able to catch on fast.
This book and its stories are very short and simple. The reading is fast and young...younger than even some of the earlier Potter books. The tales are whimsical and entertaining, but nothing extraordinary or earth shattering. I've read a bunch of fairy tales over my life and actually last year I read a big collection of "Grimm's Fairy Tales", so I found a lot of common/reused elements. Some of the stories felt very familiar, but I couldn't pinpoint any plagarism per se...just reuse of common elements for fairy tales & fables. I'm sure she had particular stories as inspiration for her tales and somebody familiar with them can likely see the resemblance.
The one tale I had been told was "borrowed" from something I read was the tale of the three brothers which had supposedly been a sort of remake of Chaucer's Pardoner's Tale. In each of the tales, there are three brothers who meet and 'cheat' death. That's about the extent of the similarities. The character development and the plot itself are very different between the two tales. Frankly, I enjoyed Chaucer's more. :)
Overall, while the stories were fun and whimsical for a bedtime reading, they were entirely unremarkable. The only real "meat" of the book is the inclusion of Dumbledore's commentary on each story. While fairly superficial and obvious as far as commentary goes, it was interesting and fun to essentially participate in a literary discussion about tales of magic from within a world that magic really exists. Even then, the commentary isn't meaty enough to turn these Tales into a "Great" book.
I applaud Rowling for her creativity in writing a book within this "form"...a backlog of fairy tales from within the wizarding world accompanied by a commentary from a wizard/professor. Personally, I would like to have seen more in-depth treatment in the commentary (since that's the real "novelty" here). Additional illustrations may have made this better as well...the stories are clearly young children's stories, but the book presentation makes it difficult to present to very young readers. I'll probably try reading a couple of the stories to my kids...not sure how it will go over since they are really so bland and underdeveloped.
It's worth the quick read, but (unless you just want to contribute to Rowling's charity), I can't really recommend shelling out to buy it.