"Show, don't tell."
This is possibly the most oft repeated, best known bit of writing advice ever uttered. But what does it actually mean? Aside from the occasional illustration or diagram, writing is not a primarily visual medium. You are very restricted in what you can actually show. Typically, it breaks down into a metaphor for things like "give good description" and "let the reader make their own inferences"; i.e. "don't be straightforward and boring".
But there is one thing that you actually can literally show in writing, without resorting to illustrations or diagrams--one thing which nevertheless is fairly consistently ignored by most proponents of the "show, don't tell" mantra: The language itself. The language you are writing in, and the language your characters speak.
There is, however, another bit of advice which seems to preclude showing off the manipulation of language itself as a literary device in prose: that being that the language should be invisible. Ideally, the reader forgets that they are reading, becoming immersed in the story. And it turns out that things like accurately transcribed, realistic dialog, accurate phonetic representations of dialectal speech, and similar uses of showing language are super annoying and hard to read! But that does not mean that you can never show language at all--it just means that you have to be careful. When appropriate, doing so can be very powerful.
Showing and even calling attention to features of language itself is powerful because language is intimately tied up with personal and group identity. At the simplest level, this is why good characters have distinct voices; personal identity comes through in the sometime tiny idiolectal differences in how people use their language, making them identifiable even when you can't hear their literal voice. Being able to write distinct voices, different the authors own natural voice, such that the reader can tell who is speaking without the need of dialog tags is a relatively rare but extremely valuable skill, and it is all about literally showing rather than telling.
But, the significance of language to identity goes much deeper than that. Beyond individual voice, peoples' choice of style, dialect, and even what language to speak in often hinges on establishing, or refuting, membership in a group. This is a large part of the function of slang--using it to show that you're part of the "cool" crowd, watching who doesn't use it, or who uses it incorrectly to identify outsiders to your peer group, or even refusing to use it to distance yourself from that group.
One of the best examples I know of of using language to establish identity comes from the film Dances With Wolves. At one point our protagonist, John Dunbar, has been taken prisoner by the army he used to be a part of, and is being interrogated--in English, of course. Now, John is a native speaker of English, and he is clearly capable of answering in English. He could simply refuse to speak. He could say "I refuse to answer your questions", or any number of other things. But what he actually says is:
"Sugmanitutanka ob washte..."
(Followed by some additional words of Lakota which I have not been able to find transcribed.)
Through subtitles, the audience knows that he is telling his captors "My name is Dances with Wolves. I will not talk to you anymore. You are not worth talking to."
Now, imagine if he simply said that, in English. Would it have nearly the same emotional impact for the viewer? Would it have the same effect on the other characters? No, of course not! By his choice of language, John is communicating his changed sense of identity--that he now considers himself not an American soldier, but a Lakota.
In films and TV shows, if you are going to portray linguistic diversity at all, you basically have no choice but to, well, actually portray it. I.e., have the actors actually speak a different language! (Even in Star Trek, with the conceit of the universal translator in effect, they at least have the alien characters speak gibberish in those rare instances when the translator breaks.) The complexity of ensuring the audience remains engaged, and the extra costs involved, more often than not result in simply avoiding or ignoring issues of linguistic diversity, but if you're going to do it, you have to do it. And when the details of the story make it implausible or politically unwise to use a real human language, you get someone to make a conlang--hence Klingon, Na'v, Dothraki, etc.
Writers, on the other hand, have a cheat. You can always just write, "My name is Dances with Wolves," he said in Lakota, and never have to learn or invent a single word of another language, or figure out how to keep the reader engaged. The language remains invisible. But you have then committed the grave error of telling when you could have shown! Indeed, of telling in the one singular situation where literal showing is actually possible!
"But," you say, "then the reader won't understand what's going on!"
Well, for one thing, maybe that's the point. Sometimes, the narrator or viewpoint character won't understand what's being said, and the reader doesn't need to understand it either. There may be legitimate disagreement on this one, but consider: is it better to write something like:
She said something I couldn't understand, but seemed to be in distress.
or something like
She said something like "Pomogitye! Moya sobaka gorit!", which of course I didn't understand a word of, but I could tell by her tone she was distressed.
Personally, I'm inclined to go with option 2. And if the reader is supposed to understand what's going on? As a writer, you have it so much easier than the film makers! They have to resort to subtitles, which distract the viewer from the scene. But your readers are already reading! Sticking in a subtitle costs you nothing!
"Sugmanitutanka ob washte..." John said. My name is Dances with Wolves.
And you don't need to be J.R.R. Tolkien to do a good job with a conlang in a story. In fact, while Tolkien was a fantastic conlanger and worldbuilder, and while I may be metaphorically burned at the stake for daring to say this... Tolkien wasn't really the best at integrating different languages into his stories. Dropping in a page of non-English poetry every once in a while, while exciting for language nerds like me, generally results in readers just skimming over that page, even when the reader is a language nerd like me.
So, writers: consider the languages your characters use. Consider actually showing them. And, if appropriate, consider a conlang. If you're not up to conlanging or translating yourself, help is easy to find.