Here are two questions. One is marked as "Watched" for me:
I did read both questions and follow none of them, so it's not about reading or following.
What exactly does the "Watched" mark mean?
Note, as of January 26, 2022, the peepee colored watch tag has been removed.
See this meta: New post summary designs on site home pages and greatest hits now; everywhere else eventually
Previously, questions with a watched tag were given a slightly darker background shade (see my answer here for reference), and now instead of that nice, subtle highlighting of watched questions, you get this ostentatious peepee colored tag.
As you can probably tell, the changes have not gone over well. Twelve hours ago that announcement at meta.se had a score of +50; as I am writing this it is around -150.