I first encountered the word at age thirteen, when my eighth grade English class was collectively reading an English translation of Don Quixote. The word was spoken by Sancho Panza, as an expression of annoyance at Don Alonso’s habit of waxing prosaic when given the slightest opportunity.
Known the word for years – at least since I was a teenager, back in the '70s – but I’ve never used it and don’t think I’ve ever heard it used.
That word “prosaic” you have used. I do not think it means what you think it means.
As to palaver:
Count me as another who’s read it in mostly British or archaic contexts but has never heard it and has probably never used it.
Prolix, mayhap. 
I meant in the sense that he wasn’t as lyrical as he imagined, but fine: waxing eloquent.
Parabola, parole, parlor, parley, etc.: Drilling farther down into the etymology, it all goes back to Greek para ballein, literally ‘to throw beside’. Setting ideas side by side to compare them. Maybe it’s significant that one of the Ancient Greek meanings of paraballo is ‘vie with one another’. It has a lot of different meanings deriving from “throw beside,” some of which are relevant to this thread and others not so much.
Most sources have palaver as coming from Portuguese palavra for word or speech. Whether that actually came from para ballein I don’t think is relevant, because palavra would have have simply meant “word” or “speech” at the time when it became borrowed as palaver.
This is off-topic, but I wanted to note that you have come to my attention lately as a Doper who is extremely well-versed in matters of language, and I’d like to express my gratitude that you so freely share of your knowledge with the rest of us.
I find myself wondering if you would describe yourself as a linguist or as a philologist?
Brit here: agree with the posters who say it means a bit of a to-do, a kerfuffle, an unexpected/unnecessary fuss etc. And the phrasing ‘well that was a bit of a palaver’. I’ve never heard of it meaning ‘a talk’ or ‘a chat’. I’d say it’s a bit old fashioned and I can’t imagine many people under 50 would use it, ever. But that’s just my guess.
Thank you, it’s very kind of you. I study the science of linguistics, I enjoy the avocation of philology, and I earn money by translating. I think of philology as historical linguistics applied to literature; Studies in Words by C.S. Lewis being the perfect example (e.g. it delves into the deep connection of nature and kin; fascinating stuff).
Just be glad I didn’t take it all the way back to Proto-Indo-European! 
For what it’s worth, whenever you show up I’m pretty happy too, @Johanna. You know your stuff and share knowledge well and gracefully!
I think I first heard this from the Decemberists’ “On the Bus Mall”, so yes. Come to think of it I think I heard of this band first from SDMB…
I lived in West Africa as a boy and palaver was a description of a discussion between a group of native tribal elders. These discussions tended to be noisy and heated.
So a palaver was a noisy, heated group discussion.
I’ve seen the word from time to time, but I’d not really known the definition. I’m not sure that I’ve ever heard the word spoken.
Exactly what I meant in my post upthread
Off-topic, but seeing “parabola” reminds me of P.G. Wodehouse and his line “across the pale parabola of joy”, a brilliant parody of early 20th century poetry. It’s in one of the Psmith stories.
I wouldn’t be surprised to find “palaver” used by Wodehouse.
Australian here - Americans really need to grasp that English is the language of the Commonwealth as much as it is the language of the UK - and palaver is understood here too, though not really a common term.
I associate it with Polari though that may or may not be accurate.
I always figured it was British for someone with a lot of friends.
You know, a real pal 'aver.
I’d not heard it until I moved from the US to the UK. It’s always used as “what a palaver” similar to “what a full” or “what a ball ache”.