In American, 'quite' is often an intensifier but not as strong as 'very'. (Thus, if you're improving you can go from good to quite good to very good.) In British it's almost exactly the opposite. It's close to 'rather' or 'pretty' (used as adverbs). So if you're improving you could go from quite good to good to very good.
On both sides of the Atlantic, it can also mean 'completely' (as when you're not quite ready). How the 'completely' meaning is related to the others is something I've always wondered about.
I wonder if that last use of 'quite' is an NPI [NB: I do not necessarily endorse Ladusaw's account, mentioned at the end of that post]. NPIs are phrases like 'at all' or 'either' that can occur only in certain environments, like after a negation or in a question. e.g.
I'm not at all ready. Are you at all ready? *I'm at all ready
It seems to me that the most natural uses in the UK of 'quite' to mean 'completely' are in NPI-licensing environments, like "I'm not quite ready" or "Are you quite done?" This accords with something Tad Brennan (if I remember correctly) told me when I was at Cornell last week, which is that "not quite" means the same thing in the UK as it does in the US, even if "quite" doesn't. But I don't speak UK English, so I don't know.
I thought for a moment that the constant utterances of "Quate" by Tubby Vanringham's fiancée Prudence might indicate that quite-as-completely can occur in positive contexts, but it would make sense to utter "Rather" in the same contexts, so that doesn't show that this isn't quite-as-rather.
Apropos of "quite," when I read Barbara Pym's An Unsuitable Attachment I was bemused by the description of Rupert Stonebird as "quite good-looking." It was obvious from everything else in the novel that he was just a decent-looking fellow who wouldn't stand out in the crowd. It wasn't till sometime after Bill Clinton's "quite" flap that I realized that that's what "quite good-looking" means in the UK.
Checking the link, what Chris Bertram says about quite sure would seem to undermine the thesis of this whole post. Oh well. [And he elaborates here; my new theory is that speakers of UK English are mad.]
From the brownsauce.org blog (what, you don't read a blog devoted to HP sauce?), try reading this aloud:
Police officers rushed to hospital after a suspicious substance was thrown through a car window were released when it was identified as HP sauce.
I was completely and utterly garden-pathed by that sentence. It may not help that it's in journalistic shorthand; I think outside a newspaper "Police officers who had been rushed to hospital" would be more likely (though I don't say "to hopsital" either). Applying this to my previous ruminations about garden-path sentences will be left to the reader.
It's a shame; the sentence would've been deadpan funny if I hadn't had to spend so long figuring out what the main verb was.
I'm pleased to announce that "The (mostly harmless) Inconsistency of Knowledge Ascriptions" has appeared in Philosophers' Imprint; you can read it here, or find the PDF and links to individual pages this page. No subscription or anything required; it's available to anyone with an internet connection. (The first link may not be stable -- I'm not sure how the URLs for the page viewers work -- but the second should work, and you can click on "page 1" to go to the page viewer.)
This was a pretty major undertaking for me, and I think the theory of knowledge it presents is pretty novel (though Stephen Schiffer has argued for something similar). I won't pretend that my arguments are knock-down, but one of the referees said something like "Even if I don't agree with the conclusion, I think it'd be good to have these arguments out there," and I'll happily accept that. Anyway, I do agree with the conclusion. In addition to all the acknowledgments in the paper, thanks to the Imprint for being a great online journal (and thus a good place to publish long papers like this) and also for being extremely patient with me on several occasions.