Foreign untranslatable words and phrases
This is a nitpick, but linguists today believe that there is no such thing as an untranslatable word. It might not be able to be translated quite as nicely or poetically, and a single word translation will not bring across the full connotation and denotation, but the translation still exists in any natural language. Often you will read articles talking about an "untranslatable word" and then translate it in the next sentence, like https://www.boredpanda.com/untranslatable-words-found-in-translation-anjana-iyer/ (the first DuckDuckGo result for "untranslatable word"). I agree with your concept of some ideas being unable to be understood without context though.
I guess this is a matter of opinion on how much explanation makes something "untranslatable". For example, maybe it takes 1000 words to give enough context to adequately convey the meaning of a word with a very precise meaning in another language. Is this word "translatable"? In a certain sense no, because making sense of it required giving the person a lot of new context that they didn't have before such that they could make sense of it that was beyond simple reference to existing concepts they had. Obviously the other end of the spectrum where there are words that are literally impossible to explain don't exist or else even the speakers of the same language wouldn't be able to convey their meaning to each other, so it seems to me fair to say some words are untranslatable if by that we mean unable to provide a direct or simple translation on the order of using something up to the size of a phrase to capture the original meaning of the word.
I think some big life events fall into this category: being married, having a kid, having a close loved one pass away, dying yourself.
I'm surprised no one has mentioned natural semantic metalanguage at this point. Research indicates that all humans share a common frame of core concepts. It shouldn't be too surprising if one considers our brains to be similarly engineered.
My question is that, if one cannot describe something, did you , in fact,understand what you were experiencing?
Indescribable things cannot be described in a finite number of words. That's because each one contains an infinite quantity of information.
I would disagree with that. Suppose you take a plank scale recording of the entire quantum wave function (within Hubble volume), along with some kind of look at this bit pointer. (A few web pages about the colour red should do it.) This contains all the information about the colour red. The whole universe is there to tell you the clustered structure of thingspace, the extra article is so you can pick out the "red" cluster as opposed to the "turtles" cluster. Whether or not there is any way to get this info into the brain of a blind human is anther question, but the info is there. A complete description of "the sensation of red" is finite. Much of the info could be got into the brain of a blind human, say with a series of talks on optics, vision ect. However the brain is incapable of doing arbitrary format conversions.
Whether or not uncomputable numbers require infinite info is getting into weird subtleties of logic, model theory ect.
Some things can be described only via experience.
Other things cannot be precisely described at all.
Indescribable things cannot be described in a finite number of words. That's because each one contains an infinite quantity of information. I don't mean they convey this information all at once (except for noncomputable numbers). Rather, they open up a new channel of information.
Opening up a new channel of information is mathematically equivalent to adding an input node to a neural network. This is a totally different process from training a machine learning system. When you train a neural network you adjust the weights of the connections between neurons to solve a problem. Adding hidden nodes amounts to basically the same thing. Adding an input node to a neural network unfolds a new dimension of the problem space thereby adding information for the network to work with. In other words, adding a new input node doesn't improve your solution to a problem at all. It makes the problem easier instead.
For example, the traditional Chinese method of teaching strategy involves memorizing ancient Taoist texts. This pedagogical technique is off the radar of modern MBA programs for reasons independent of its effectiveness. The "memorized passages of concise time-tested wisdom" input node is just missing.
You can't tell someone an indescribable thing but you can tell her where to look. You can tell someone to identify the color of blood, listen to a piece of music or stare silently at a blank wall until you see the essence of reality.
The arts of war…cannot be ignored.
―first line of Sunzi's The Art of War
Where else should I look?