What precisely has been going on at Goodreads? I'm glad you asked.
Here's my take. 
Please note that it's a work in progress as I try to fill in some of the pieces I'm missing.
What started this?
On September 20, 2013, GR decided to institute a new rule that "reviews should be about the book." (What motivated this? We'll get into that later.) The only notification of the change was in a thread in the GR Feedback Group (Link to the thread). Without warning, GR deleted a set of reviews and shelves it decided were not in line with this policy. According to GR, this wasn't censorship:
[The reviews deleted] are reviews of the author's behavior and not relevant to the book. We believe books should stand on their own merit, and it seems to us that's the best thing for readers.
Someone used the word censorship to describe this. This is not censorship - this is setting an appropriate tone for a community site.
More Shelf Deletions
As can be seen in the Feedback thread, members weren't thrilled. The outcry--and the obvious lack of clarity in the policy-- caused GR to hedge and revise again and again. It apologized for summarily deleting shelves and posts, but said that the posts were gone and that they still violated content, so would not be reinstated in any case. At the same time, it continued to delete shelves, reviews, and Listopias, including "Badly-Behaving-Authors", "Objectively-Bad-Books", and more. See Literary Ames' post for links) Members started getting creative. Since "due-to-author" and "badly-behaving-authors" weren't allowed, what if the shelf was renamed "Hormel"? GR responded that such shelves were still Thought-Crimes: GR would interpret the contents of a shelf to decide on whether it would be allowed to stay. It proceeded to delete shelves called "Hormel" (see post 2627) , as well as Carol's "author-behavior-unacceptable" shelf (fittingly, the post on the Feedback thread appears to have been deleted,). This new policy of mind-reading led to a certain number of false-positives (e.g. the deletion of a shelf called "Tain" in reference to Irish mythology, and the deletion (post 3431) of a positive shelf called "shizzle" ) Originally, a "due-to-author" shelf was deleted (Steph Sinclair); at some point, when it began to see the negative backlash from mind-reading policies, GR reversed its opinion on this one.
Apparently to GR's surprise, a large number of people appear to dislike arbitrary censorship and an attempt to control what they are allowed to consider in a consumer decision. According to a Salon article, the group that reacted were mainly the high-content-creating "top 1%", most of whom had never even participated in the "badly-behaving-author" war. Why? It came down to a gut reaction against censorship; a sense that, in the increasingly tense author-reviewer interactions, GR was taking sides; a feeling that this was the first move in a game to turn reviewers into monetizable Amazon content; a sense of betrayal; an anger against the absolutely inappropriate way that GR initiated this.
The GR-reviewer battle ramps up
Reviewers were angry. GR was unresponsive. This is not a recipe for compromise.
[R] In protest, some users started posting reviews involving author behavior in which no one could dispute the importance of author behavior. (A personal favourite is Mike's review of Mein Kampf:"This author is such a dick. I'm not even going to read it!") They then encouraged flagging of these reviews to demonstrate the flaws in the system; see Manny's post, which includes some of his flagging messages.
[G] GR's response? Delete and/or ignore and threaten account deletion to get the message across. (You can read the reviews at the "hiddenreviews" Tumblr, which has tons of posts, opinion pieces, and (yes) the deleted reviews.)
[R] Other reviewers started posting reviews that were tangentially related to the books, but mainly discussions and criticisms of GR's actions.
[G] GR's response? Since these did not actually violate the updated guidelines, GR changed the guidelines again and deleted the reviews as "potentially off-topic." Threats of account deletion ensued. (LiteraryAmes' blog has the details.)
[R] Reviewers came back with the hydra effort, in which deleted reviews were reposted (sevenfold, one presumes?) by other reviewers. (Link to Carol's reposting of Manny's and Clouds' "call to hydra"; screenshots of Manny's "hydra" review on GR)
[G] GR's response? A new rule against "non-original content," despite explicit permission from the original poster. (the same post by LiteraryAmes has examples of these as well; Ceridwen also has a great summary)
[R] Reviewers then noticed an interesting loophole: while reviewers are heavily censored, authors are allowed impressive freedoms within their books. With the joys of self-publishing, the difference between "reader" and "author" is a single upload. So some reviewers decided to put together a book about censorship and GR. (Here's the post where Clouds proposed the idea.)
[G] Despite a policy that absolutely forbade deletion of books....GR deleted the book.
[R] Reviewers put together a second book, called Off Topic. They put it on Lulu, where it was indisputably just as valid as all the other indie books on GR. (You can read Off-Topic right here.)
[BA] An author tagged as a badly-behaving author petitioned Lulu to get the book removed. It was. (Lulu's concern was that it contained the names of the authors of the 21 initially deleted reviews.)
[R] During all of this, reviewers continued to flee GR for BookLikes and other alternatives, remove their reviews, and delete their accounts.
What caused this?
It's hard to know, but we do know that a few things have changed.
GR was bought out by Amazon.
Forbes posted an article in which they claimed the "hidden benefits" are the "creditable reviews" (hah), but also the "data mining", "influencer targeting", and "promotions hub", and, right before the review-burning, Amazon announced that GR reviews (and, presumably, shelves and Listopias) would be integrated with the new Kindle.
Second, in the last few years, GR has been gaining a larger and larger percent of its profits via its Author Program. It has begun to speak of the site as a "site for authors and their fans" rather than "a site for readers." He stated on video (3:39) that
"We're in the business of helping authors and publishers market their books to readers."
The change in direction is visible in presentations that market GR to authors, where (in "Helping Readers Discover Your Books") he said that "Goodreads Is A Social Media Platform For Authors", "Your goal is to get reviews, especially early in the life of your book. Reviews help readers discover your book. They help readers decide to read your book. Goodreads reviews work harder for you.") He also (In PubWest 2012: How Readers Discover Books Online) explicitly tells authors to "post your events and invite your Goodreads friends...[in an example] messaging friends located in each city she visits on tour" "join groups to build your network", use GR for "fan interaction", "follow the fans." GR started marketing themselves to authors ("How Authors cam promote their books and build a tribe"), saying, "the best place to meet Goodreads members is in groups" and "once you've hooked a reader, they will come back for more."
Dousing the Flamewars
Third, GR has been receiving consistently bad press over apparent "bully reviewers." The recent incident with Lauren Pippa/Howard (more below) may have been the last straw. Directly before the "Important Announcement," Kara posted on a thread complaining of cyberbullying on GR (not clear from authors or readers, but the complainant is not a writer) to say that "someone is now working on this." They have also made changes in an attempt to prevent author meltdowns.
Other reasons? Steph Sinclair talks about growing tension, "be nice", GR shifts in direction, and poor journalism.
Bully reviewers? Bully authors?
There's been a lot of press about GR and "bully reviewers." While I can't speak to all situations, in all the cases I've seen, the author responded negatively to a critical review and/or claimed it was a "bully review." After an author response, readers and reviewers shelved or one-starred the review in retaliation. There's a lot of debate about how writers and readers should interact in their shared space, and I don't know what the answer is. However, in these days of social media, small person-to-person tiffs suddenly can become very large-scale coordinated protests (or attacks, depending on your perspective,) with authors tagged as "badly-behaving" and reviewers being denounced on STGRB.
GR's new focus on attracting authors has changed the site in ways that many reviewers find detrimental. "Spamming" in groups, where authors plug their books continuously and use any excuse to reference their own books, feel increasingly common. Messages, event invites, spam friendships, and more are constant attempts to push the reviewer to buy, read, buy, read, review, review, review! Granted, there really are very few "badly behaving authors," but with GR encouraging the very "spamming" behavior that many readers find irritating, things have become increasingly tense on the site. Speaking from personal experience, about half the notifications I see from my groups are from self-promoters. Because of this, I think reviewer reactions to "bad behavior" from authors have become faster and harsher.
A term you'll hear thrown around a lot is "STGRB" or "STGB." It stands for "Stop The Goodreads Bullies," a group set up a year or so with the professed aim of standing up against all the "bully reviewers." ("Bullying," in this terminology, appears to include giving critical or 1-star reviews and/or reacting harshly to authors who attack reviewers for giving 1-star reviews.) STGRB "stands up against bullies" by (to quote them from an interview) "giving them a taste of their own medicine." In their first salvo, they "doxxed" a large group of reviewers--that is, they posted as much personal information, including profile pics, doxxing them ("posting the Bullies' profile pics, name, and location"). STGRB has gained a great deal of legitimacy after Huffington Post allowed them to post an opinion piece, despite HuffPo's later apology and many guest posts repudiating STGRB. While STGRB later denied doxxing, there is plenty of evidence to the contrary. Personally, I've lost track of what's happened on STGRB since then, but a cursory glance indicates the tone remains the same.
Lauren Pippa/Howard and the Shelves of Doom
I can't pretend to know how often reviewers really do engage in cyberbullying, but some of the notorious cases have been shown to be false, including the one that may have precipitated the change in policy. In early September, several news articles reported that a fledgling indie author, Lauren Howard, was pulling her books because of threats of rape and murder on GR. Upon further investigation, it turned out that the journalists had failed to perform any fact-checking; it was discovered that Howard had reacted to a 2-star review of her unreleased book, insulted GR librarians when they told her they could do nothing, and received "badly-behaved-author" tags in response. (See summary, with screenshots, from darkwriter67.) Some of these tags did not have particularly tasteful names, but none of them were threats. Howard subsequently recanted, blaming her overreaction on PMS. Unfortunately for reviewers, the retraction of the articles did not make a splash in the news, and the death-rape-threat-bully-reviewers image remains.
Refusal to make a site announcement
Despite the tens of thousands of comments on the feedback thread and many users' obvious interest in the situation, Goodreads claimed that "these changes affect only a very small number of our members" and that they therefore would not be making a site announcement.
And yet (via Debbie's Spurts) site announcements can be made for more important things--like kindle rollouts.
Blame it on Booklikes
Along with many other issues with the site itself, other reviews started disappearing without warning. Goodreads claimed that it was due to BookLikes -- although, as one blogger pointed out, even if BL was responsible, (HELP! I CAN"T FIND IT) anyone who is careless enough to release deletion permissions with their API kind of deserves what they get. (Report by the-digital-reader)
Kindle Integration Woes
(From KrazyKiwi) GR's careless integration with Kindle caused the painstaking work of many (volunteer) GR librarians to be destroyed--but that's OK, because they can always get all those volunteer librarians to do it all again, right?
During this debacle, many people (including me) experienced issues with updates, not receiving update emails, likes not updating correctly, and more.
As of Nov 25,2013, weekly "top users", "top readers", "top reviewers", haven't been updated since Oct 06, "weekly most popular reviewers", "most followed people this week", "top librarians this week", and "weekly top reviews" haven't been updated since Oct 05, which is, incidentally, when hydra reviews and protest reviews started gaining popularity. However, while I noticed protest reviews were actually in the top-50 reviews earlier, it looks like at least 5 have been deleted. (From Debbie's spurts) In mid-November, GR "temporarily disabled" exporting
But never fear! GR is working on what matters! (From Debbie's spurts) Goodreads introduces mobile ads.
So welcome to a new GR, where you, too, can join an author's "tribe" and help GR with their "business of helping authors and publishers market their books to readers." It's a brave new world out there; our new, happy life.
It's lucky we have GR to tell us what to think.
After all, we've always been at war with Eastasia.
 Oh, you didn't? Accidental click or something?
 Just to be clear, I haven't been personally affected at all. I haven't had a single review or shelf deleted, and have never even had an angry interaction with an author. My issue with this whole thing is what I see as GR's betrayal of trust, its disingenuity, and the precedent these action create.
 Personally, I didn't come to GR to be in anyone's "tribe".
P.S. Thanks especially to Debbie's Spurts(donealrice), Batgrl (batgrl), Themis-Athena (themisathena), and Reading Jane Austen in Boston (e) for pointing me to so many great links. I'm not a blogger and very new to blogging etiquette. If I have cited posts wrong, or you don't want me to link to you, or you have any links you think I should add, please let me know!!