"In no uncertain terms" is an idiom in which the "no" and the "un-" cancel, so that the result means something like "in very specific and direct language", "very clearly", "in a strong and direct way", or perhaps "emphatically". In other words, "in no uncertain terms" means "in certain terms", construing "certain" as in certainty. The earliest example that I've been able to find is this sentence from the Chicago Tribune, July 20 1863:
Our dispatches contain another circular from the Provost Marshal General's office, and accompanying, the voice of the Government, couched in no uncertain terms, that the draft will be enforced in every loyal State, without fear or favor.
And "in no uncertain terms" is still being used that way, as in this example from today's New York Times:
After last week, the question now is: Why am I writing a post this week instead of sleeping?
When more than 200 people tell you, in no uncertain terms, that the first step to dealing with the exhaustion incurred when a child does not sleep is to find ways and moments for you, yourself, to sleep, that’s a fair question.
But recently, through the miracle of misnegation, this elderly cliché has found a new role in life.
Cynthia McLemore spotted an example Ben McGrath's article "Does football have a future: The NFL and the concussion crisis", The New Yorker, 1/31/2011:
Please ignore the "beg the question" usage — or read this post if equanimity in the face of question-begging is beyond your powers — and contemplate the captalized assertion that "IN NO UNCERTAIN TERMS DO I BELIEVE THAT WE SHOULD OUTLAW OR "WUSS DOWN' CONTACT SPORTS".
If we temporarily leave aside the subject-auxiliary inversion ("do I believe" rather than "I believe"), we take this to say the opposite of what Dustin Fink means. Using the traditional interpretation of "in no uncertain terms", it seems to mean "Emphatically, (do) I believe that we should outlaw or wuss down contact sports", whereas he clearly means "In no way (do) I believe that we should outlaw or wuss down contact sports".
Let's note that Dustin is not alone in using "in no uncertain terms" to mean something like "in no way", as a search for "in no uncertain terms do I" demonstrates:
I am 25 wks pregnant now and I have told my partner in no uncertain terms do I want another one that close!!
One thing to id like to make clear i do know this person and in no uncertain terms do i support his group,in fact he sickens me.
In no uncertain terms do I want my tax money used to issue school vouchers.
i hope that explains that in no uncertain terms do I disagree with ben regarding our military nor do i disagree with him about the situation
thirdly, in no uncertain terms do I excuse rape, or will ever excuse rape
in no uncertain terms, do i want her kissing any of my children on the lips, least of all my infant - ever
But now let's get back to that subject-auxiliary inversion. It's an interesting characteristic of contemporary English that with initial negative adjuncts, subject-aux inversion happens just in case the negation takes scope over the following clause. Thus consider this pair:
(a) With no friends, John would be happy.
(b) WIth no friends would John be happy.
Sentence (a) means roughly that if he had no friends, John would be happy. In that case, the scope of the negation is limited to the interpretation of the prepositional phrase.
Sentence (b) means roughly that there are no friends such that John would be happy if he had them; and in that case, the negation takes scope over the interpretation of the whole sentence.
(This curious connection between form and meaning was the subject of one of my first published papers, "On conditioning the rule of subject-auxiliary inversion", in Ellen Kaisse and Jorge Hankamer, Eds., Papers from the Fifth Annual Meeting of the North East Linguistic Society, 1974.)
Note that when the people take "in no uncertain terms" to mean something like "in no way at all" rather than "emphatically", they uniformly seem to use subject-aux inversion, as illustrated by these web examples:
Admittedly, the No. 4 seeded Eden Prairie High School boys soccer team opned Section 2AA play Thursday with a chip on its shoulder. In no uncertain terms did they think they deserved the No. 4 seed and if Bloomington Kennedy, Thursday's opponent, was in any way responsible, they were going to pay.
In no uncertain terms will I ever support any legislation that infringes on the rights of law abiding citizens to keep and bear arms
In no uncertain terms does the mayor condone any behavior of this sort.
In no uncertain terms should hitting your dog be considered appropriate punishment.
In contrast, when people mean a clause-initial instance of this phrase in the conventional, old-fashioned way, they don't invert:
In no uncertain terms she blamed “that spoiled Addison girl” whom Elijah D. had married for the unwashed aspect of that “somber hard-faced boy".
In no uncertain terms, he wants the press to know that Oswald isn't being mistreated.
In no uncertain terms he told them that Jesus is holding everything together!
You'll be pleased to hear we're committed to providing the best of everything and in no uncertain terms we feel our unique product offers the best solution …
In no uncertain terms, he reeled off the news about Iran, why it was bad, what it meant for the markets, why it wasn't priced in to the markets, and what would probably happen.
[Update — Those of you who have checked out Dustin Fink's Concussion Blog will have noticed that in addition to providing excellent information about the issues around concussions in general, and sports-related concussions in particular, it's overall quite a rich source of syntactic innovation: "All information and photos are brought to you via the blog is for the intent of education and communication of concussions"; "WE JUST NEED TO BE EDUCATED AS TO PREVENT LONG TERM EFFECTS AND DEATHS"; "By developing this blog it is the hopes that we can create a community for support, education and communication for this rising epidemic"; etc.]
[Update #2 — The Google n-gram viewer seems to confirm that the phrase "in no uncertain terms" originated in the mid-19th C., and came into widespread use after 1900:
I'm not sure how to explain the apparent fact that usage leveled off around the end of WWII — as often with the n-gram counts, it's not clear to what extent this is a change in the language and to what extent it's a change in the mix of books in the underlying corpus.
But checks with other sources (e.g. COCA and BNC) do confirm that "in no uncertain terms" has in recent decades become somewhat more common than "under no circumstances".]