The phrase means “available for sale” or, more generally, “available.” The first OED citation is from the (London) Daily News in 1881: “Old wheat scarce and dear. Very little barley on offer.” But using Google Books, I came up with an example more than fifty years older, from a September 1826 issue of Cobbett’s Political Register:
But in any case, the phrase didn’t cross the Atlantic for another century or more:
A relatively early use came in the New York Times in 1990: “Tens of thousands of Apple Macintosh users visited the Macworld trade exposition here earlier this month, examining the hardware and software on offer.” It arrived in the New Yorker through British writers—Kenneth Tynan in 1977 and Salman Rushdie in 1992—and was first used there by an American one, Hendrik Hertzberg (using the magaqzine’s famous editoral “we”), in 1994: “We know, for example, that there are people who picked up their first copy of The New Yorker on account of a story or a “casual”–on account of something by O’Hara or Cheever or Salinger or Perelman or Munro or Updike–and only later, and gradually, became aware that other kinds of writing were on offer in these pages too.”
But it’s all over the place now. The Times used the phrase 112 times in 2021, from to January 21 (at a hair colorist’s studio, “Cappuccino and mineral water were served, and tuna and watercress salad was on offer”) to December 21 (“While the Omicron variant has thrown many people’s New Year’s Eve plans into doubt, there’s no shortage of events on offer in the televised realm”).
notoneoffbritishisms.com 
In the UK I’ve only heard this to mean something is marked down in price. Like “on sale” and not necessarily “for sale”. Interesting to see it’s been used in other ways too.
Seen both.. the “on sale” version of “on offer” having presumably been shortened from “on special offer”
I’d say it’s used in either sense here in the UK.
Here’s something I wrote about this some years ago. Please remember that my default position is a semi-serious objection to any British usage in American.
Objectionable British import meaning “available” or “for sale” or “on sale.” This term has gained purchase despite its cost to meaningful American dialogue.
“Gained purchase” a Britishism?
What I wrote was about “on offer,” but I don’t think of “gained purchase” as a Britishism. In the sentence, I meant its friction-related sense, but also a linguistic wink– along with “cost”– to the “on sale” meaning of “on offer.”
“objection to any British usage in American.”
Personally, I have the opposite view, the British use of language is so much more clever and expressive. Americans can only benefit from enlarging their lingusitic perspective.
Nevertheless, I have to give you a like for the cheeky use of “gained purchase”.
Thank you. Although I stand by my stance, I agree that there is a (much, much smaller) list of Britishisms that is beneficial and an improvement on American. Spelling judgemental this way, for example. I also think forgot and got are more sensible than forgotten and gotten. Things like that.
If you are from Australia and not the Emerald City, Peter, I can only assume that you are, as we Americans like to say, “taking the Mickey” when you say something like, “British use of language is so much more clever and expressive.” The only possible response to something as unmeasurable as that is, “Prove it.” But that’s not my point, anyway. I’m not saying American is better than British, but I am saying– only half-jokingly– that it is better for Americans to eschew Britishisms.
On Fri, Sep 2, 2022 at 1:14 AM notoneoffbritishisms.com < comment-reply@wordpress.com> wrote:
There’s also the form “see what’s on offer” you heard said when you want to buy something (or go somewhere) when you haven’t made plans as in “Let’s go up to the Edinburgh Fringe and see what’s on offer” meaning you will decide when you get there.
You might also apply this to a mall or market visit, say, or even as a reference to visiting a “pickup joint”.
Is “taking the Mickey” in quotes to mark the irony of claiming it as an American expression? Smiley face.
Mais oui, to cite another popular Americanism.
On Fri, Sep 2, 2022 at 1:49 PM notoneoffbritishisms.com < comment-reply@wordpress.com> wrote:
Thirty years ago I was pulled over by the cops on Marylebone Rd (the one in London, silly, not the one in March). They let me off, but warned me I’d been putting myself “on offer” (never overtake a police car, even where there are two lanes). So there’s a wrinkle on the ‘available’ meaning of “on offer”.
‘I was born in February in March, lived on a street in Roade, and died on a road in Street’ – does anyone remember the full version of this? My grandmother used to say it, and I can’t find it online.