Just so you know, I voted to reopen the question. It seems similar to my own What exactly is an “adverb”?, which came perilously close to being closed as General Reference before gaining traction and becoming my second most upvoted question.
Apropos which, I'm still a bit piqued that my Where does “Don't bogart that joint” come from? remains closed as GR. Okay - it's obvious once it's pointed out. But I couldn't easily satisfy my curiosity anywhere else online at the time, and I generally consider my google-fu to be pretty good.
As John Lawler says (and he should know! :),...
Modality is a very complex subject. It's the source of the grammatical term mood (as in "subjunctive mood"), and it also uses a special variety of logic called Modal Logic. It's precisely on target here.
Some folk here seem to think I habitually closevote questions as Too Basic, but I reject that. Mostly I think there are no dumb questions, only dumb answers. I often closevote ELU questions because I think they're not suitable for this site, and should have been asked on English Language Learners.
I've no doubt entire books could be written about linguistic moods, modality, modal verbs, etc. I don't want to see an incredibly long answer on ELU trying to cover every aspect of the concept, but it would be nice if someone could post a relatively short (but authoritative) answer. Which can't happen while the question remains closed.