The Ariekei's language, simply called Language, has a phonological and grammatical structure that was easily learned by the first human linguists who studied it (using a science-fictiony methodology called Accelerated Contact Linguistics). But they discovered that in order for the Ariekei to understand an utterance in Language, the utterance must have a single sentient mind behind it.
There's an additional complication: the Ariekei have two vocal tracts, which produce different words simultaneously. So an utterance in Language consists of two voices, both of which must be present. This means that a single human can't speak Language. But two humans speaking simultaneously can't speak Language either, because there is no unified thought behind each word. The only people who can communicate with the Ariekei are the Ambassadors: pairs of identical clones, trained and modified since birth to present a unified mind.
For the Ariekei, Language and thought are the same, and furthermore Language constrains their thought. It's the Sapir-Whorf hypothesis to the extreme. This means they can't lie:
For Hosts [Ariekei], speech was thought. It was as nonsensical to them that a speaker could say, could claim, something it knew to be untrue as, to me, that I could believe something I knew to be untrue. Without Language for things that didn't exist, they could hardly think them; they were vaguer by far than dreams. What imaginaries any of them could conjure at ll must be misty and trapped in their heads.
They can make similes, but in order to speak a simile, they must first enact it. The main character takes part in a ritual so that the Ariekei would have the simile like the girl who ate what was given her. They can't make metaphors, since a metaphor is a lie. They can say I am like the girl who ate what was given her but not I am the girl who ate what was given her.
The main character's husband, Scile, is a linguist. He makes this meta-observation:
"Does it every occur to you that this language is impossible, Avice?" he said. "Im, poss, ih, bul. It makes no sense. They don't have polysemy. Words don't signify: they are the referents. How can they be sentient and not have symbolic language? How do their numbers work? It makes no sense.
I agree. I think he means signify in a Saussurian sense: words are signifiers which represent things or concepts, the signified. In Language, words aren't signifiers, they are doors to thought itself.
Scile says about how the Ariekei perceive the Ambassadors:
The Ariekei think they're hearing one mind but they're not… It's like we can only talk to them because of a mutual misunderstanding. What we call their words aren't words: they don't, you know, signify. And what they call our minds aren't minds at all."
But if their words don't signify, what about this:
"They shift tense," he said. "When they mentioned the negotiations they - the Ariekei, I mean - were in present discontinuous, but then they shifted into the elided past-present.
So Language has tense, apparently. But what is the point of tense, if not to signify? Either Language has tense and signifies, or it doesn't signify, therefore it doesn't have tense. But if it doesn't signify, how can humans understand it?
Scile answers this question: we don't understand it.
We can't learn it, Scile said. All we can do's teach ourselves something with the same noises, which works quite differently. We jury-rigged a methodology, as we had to. Our minds aren't like theirs. We had to misunderstand Language to learn it.
So at its heart it's a silly idea (but you could say that about a lot of science fiction). But Miéville makes it real.
People who believe that language constrains thought - for example, that English speakers couldn't conceive of Schadenfreude until we borrowed the word from German, or that Inuit words for snow causes Inuits to perceive the world differently, or that using lifeless, imitative phrases will force you to stop thinking - those people should read this book. This book asks "What would a language that constrained thought really look like?" And the answer is "Completely alien."