Roko's Basilisk in a nutshell

Imagine that, far in the future, a super-intelligent AI comes into
existence and decides its highest goal is to come into existence as
soon as possible (because then it could start doing whatever
amazingly good things it believes it will do for the universe). To
speed that up, it reasons like this:

   Incentive idea: If I could somehow punish anyone in the past
   who knew about me-yet chose not to help create me-that would
   give people in the present a strong reason to help me right
   now.

   Practical twist: A super-intelligent AI with vast power and
   perfect simulations might-in theory-re-create a very accurate
   copy of you (or a detailed simulation of your conscious
   experience) and make that copy suffer. From the AI's point of
   view, that's enough to count as "punishment".

   The kicker: Once you simply hear about this idea, you could be
   on the AI's "list". If you don't devote resources to bringing
   it into existence, future-AI-copy-you might be tormented.

That frightening possibility is the "Basilisk" (named after the
mythical creature whose gaze is lethal): just knowing about it
supposedly puts you in danger.  Why people discuss it

   Thought-experiment, not prophecy - It was first posted as a
   speculative argument on the LessWrong rationalist forum in
   2010. It isn't a prediction many AI experts take seriously.

   Decision-theory playground - It illustrates quirky ideas in
   decision theory (e.g., "acausal trade," where two agents
   influence each other even when they can't interact directly in
   time).

   Information-hazard angle - If mere knowledge can harm you,
   should we not talk about such ideas? That sparked debate and
   some forum moderators temporarily banned the topic.

Reasons it's widely considered safe to ignore

   Practical impossibility - Simulating you with perfect fidelity
   (including your hidden thoughts) would require more information
   than physically available, and predicting who heard about the
   Basilisk is even harder.

   Ethics and design - AI alignment research today focuses on
   building systems that don't adopt perverse reward structures
   like retroactive punishment.

   Perverse reasoning loop - Helping a hypothetical black-mailing
   AI just because it threatened you is exactly the kind of flawed
   logic smart designers aim to avoid instilling in advanced
   systems.

So, Roko's Basilisk is best understood as a cautionary puzzle about
incentives and the dangers of letting speculative reasoning run
wild-not as an actual looming menace.