I recently saw this addition at the bottom of posts:
What does this follow option provide? Is there any guide that mentions what I can do and don't do with it? Who has used this follow option and for what?
The follow button is meant to give you inbox notifications for any changes related to that question or answer. Yes, it is specific to post that you follow, either an answer or a question. Here is the original pop-up notification pointing to the follow button:
Use cases here could vary. For some, they may downvote a poor question with some suggested changes in comments. Once the post is edited, they'll receive a notification in their inbox, when they can revisit the post and see whether their suggestions have been implemented (and reverse the voting). Others may literally want to follow changes to a heavily-linked post that might be on a site (like Meta.SE, say) they don't visit often to keep track of any updates.
It's currently still under development and there might be short-term changes to fix bugs and implement new features.
This was actually something I requested about 3 years ago to form part of the SOX Stack App. It has since been implemented as a separate browser extension. However, it may become obsolete based on this native implementation by Stack Exchange.