What would you call a word that doesn't exist in or translate well into another language?

Solution 1:

The word you are looking for is: Realia.

http://en.wikipedia.org/wiki/Realia_(translation)

Entering in the field of translation studies, a radical terminological change must be enforced: «realia», in fact, does not mean objects, but signs, words and, more precisely, those words signifying objects of the material culture, especially pertaining to a local culture. It is, therefore, necessary to distinguish realia-objects (mostly outside translation studies) and realiawords (mostly inside translation studies). Realia as the units of translation are divided into abbreviations and phrases. Also they may be divided into the geographic and ethnographic realia. The geographic realias are names of the geographic and atmospheric objects and endemic species. Etnographic realia describe everyday life and culture of nations, their spiritual and material culture, traditions, religion, art, folklore etc. Etnographic realias are those connected with everyday life, art and culture, names of residents and ethnic objects, currency units.

http://archive.nbuv.gov.ua/portal/soc_gum/Vduep_fn/2012_1/41.pdf

Solution 2:

Call me stubborn, but I don't think there exists a formal term that specifically means a foreign word, which does not have the English equivalent, or vice versa. Realia is too broad, and covers words that are also translatable. At the risk of sounding boorish, (and I have waited several days for a more definite answer,) I will stick my neck out and say, the most appropriate, and likely most understood term is untranslatability.

The Economist ¹ has an interesting article where the linguist Roman Jakobson affirms "The common trope that language X has no word for Y is usually useless (it usually means language X uses several words instead of one for Y)".

The following is taken from Wikipedia, and emphasis is mine.

Untranslatability

Untranslatability is a property of a text, or of any utterance, in one language, for which no equivalent text or utterance can be found in another language when translated. [...] Quite often, a text or utterance that is considered to be "untranslatable" is actually a lacuna, or lexical gap. That is, there is no one-to-one equivalence between the word, expression or turn of phrase in the source language and another word, expression or turn of phrase in the target language

Vocabulary

German and Dutch have a wealth of modal particles that are particularly difficult to translate as they convey sense or tone rather than strictly grammatical information. The most infamous example perhaps is doch (Dutch: toch), which roughly means "Don't you realize that . . . ?" or "In fact it is so, though someone is denying it." What makes translating such words difficult is their different meanings depending on intonation or the context.

A common use of the word doch can be found in the German sentence "Der Krieg war doch noch nicht verloren", which translates to "The war wasn't lost yet, after all" or "The war was still not lost."

Another instance is the Russian word пошлость /posh-lost'/. This noun roughly means a mixture of banality, commonality, and vulgarity. Vladimir Nabokov mentions it as one of the hardest Russian words to translate precisely into English.

Aunts and uncles

In Danish, Hindi, Gujarati, German, Tamil, Kannada, Punjabi, Bengali, Persian, Turkish, Chinese and South Slavic languages there are different words for the person indicated by "mother's brother", "father's brother" and "parent's sister's husband", all of which would be uncle in English. An exactly analogous situation exists for aunt. In Thai this concept is taken a step further in that there are different words for the person indicated by "mother's elder brother" and "mother's younger brother", as well as "father's elder brother" and "father's younger brother".

The Free Dictionary says: not capable of being put into another form or style or language; "an untranslatable idiom"; "untranslatable art" It also provides this example of usage which illustrates that language experts use the same term.

He covers public speaking, preparation/anticipating the speaker, complex syntax/compression, word order/clusters, general adverbial clauses, untranslatability, figures of speech, argumentation, formal style, diction/register, formal policy addresses, economic and political discourse, quotations/allusions/transposition, humor, Latinisms, numbers, and note-taking.

Interpretation; techniques and exercises, 2d ed by Reference & Research Book News