Usually it's for a story which simply died in queue, which as TFA notes, is the default. Occasionally it's to see if a discussion might get "re-railed" after it's gone off on some tangent --- people responding to a title or an early comment, most often.
I don't nominate my own posts, of course.
It may be a matter of how many such nominations occur, but I'd say my success rate is >50% in having those accepted.
TL;DR: it's not just dang, and normal HN'ers can participate.
And include the link in the post.
The story-ID is the numeric part of the post URL.
For this thread, where the post URL is
https://news.ycombinator.com/item?id=29024032
The story-ID is 29024032(Moderators can use the story-ID via browser extensions / bookmarklets, I just learned yesterday.)
Similarly, include the story-ID for other issues (e.g., editorialised or clickbait title, suggesting a canonical URL, vouching flagged stories, spam).