The new Operation Facebook was announced in a video posted on YouTube in which the hacktivists claim that the social networking giant is sharing information about users with law enforcement agencies and infosec companies working for authoritarian governments.
It's most likely true that Facebook is giving US government agencies access to information about users as most US-based companies do and considering the provisions of the PATRIOT Act this is probably done in silence.
However accusing Facebook of giving private companies that work for repressive governments access to its data is a bit of a stretch and so far not supported by evidence.
The group calls on all users to come together on 5th of November to kill Facebook in an effort to regain their privacy and freedom of choice. However the actual methods that will be used to destroy the world's top social network have not been revealed.
As powerful and capable as Anonymous might be in some respects it's very unlikely that Facebook will actually be destroyed. It might suffer temporary outages but something major that can keep it down for an extended period of time is probably out of the question.
The hacktivists note that user data remains in the company's possession even after people delete their accounts. It is true that deleting an account means it will no longer appear on the social network but Facebook retains the actual information for a longer period of time.
This is to facilitate later law enforcement investigations. Otherwise child molesters could target minors on Facebook and then delete their accounts to erase any evidence.
The date of November 5 was selected for the attack because it is significant for Anonymous. It is the day when the Gunpowder Plot is commemorated every year and is also known as Guy Fawkes Day or Bonfire Night. One of the signs used by Anonymous is the Guy Fawkes mask made popular by the movie V for Vendetta.