Hyperliteral translations are translations from language A to language B that try to stick to to the words and the constructions of language A, even when this means that the result in language B isn't grammatical and in some cases not even meaningful when judged with the standards of language B.
It is a known fact that languages aren't parallel. If you say that "cheval" in French is a translation of "horse" in English, then it just means that both refer to a certain fourlegged mammal. However there may be cases where 'cheval' in French doesn't correspond to 'horse' in English. Take for instance the expression "être très à cheval sur quelqu'un" = "to be strict with someone", "be a stickler with someone". Often these derived meanings have some connection with the 'core meaning' (in this case the fourlegged animal, - to be strict with someone is almost as sitting on them as on a horse), but some words don't even have a single dominating core meaning, and then there is no reason to expect that their meaning(s) can be covered by one single word in another language.
This situation is also found with grammatical constructions. For instance many languages have reflexive pronouns, i.e. pronouns that by definition refer back to an explicit or implied subject. In Danish "tage sin hat" means "take the speaker's own hat" (reflexive "sin"), while "tage hendes hat" means "take her hat", i.e. some (other) female person's hat. In English there aren't reflexive pronouns so the context will dictate the meaning in a concrete sentence.
Ordinary translations systematically try to cover up these problems by reformulating phrases or guessing at the intended meaning and choosing one out of several possible interpretations. Depending on the skill and ambitions of the translator this can mean that the general meaning is preserved, but all direct parallels between the original and the translation are lost. This can be a problem for a language learner who wants to understand the role of each element in the original version. A hyperliteral translation has no literary pretensions at all, but tries to 'imitate' the original version at all levels.
So "être très à cheval sur quelqu'un" would in a hyperliteral translation be something like "(to) be very on horse on someone", and you would add a corresponding idiomatic expression in language B if the meaning can't be guessed ('be a stickler'). However even this version isn't a perfect hyperliteral translation: the 'to' is normally necessary in English, while the French infinitive can stand alone, - therefore the word 'to' is put between parentheses. Even this simple example shows that there is some judgement involved in making a hyperliteral translation, just as in making an ordinary 'literary' translation. When explaining exotic constructions in remote languages you may even have to add morphological markers in some places. For example you could add (reflex) after 'her' in "take her hat" above. This has to be decided in the concrete case.
It is also clear that hyperliteral translations only should be used in the early stages of learning a new language. They are much better than ordinary translations to convey the structure of the phrases in the original language, but as soon as you can understand the general meaning of spoken and written texts in language A the best strategy would normally be not to make or use translations at all, except when you look up unknown words or idiomatic phrases in dictionaries and other sources. From that moment on translations would primarily be done for the benefit of others, and then it is logical to try to make translations from language A that are exquisite even in language B.
Hyperliteral translations in combination with 'normal' translations have been used in some language guides, such as the German series Kauderwelsch and the small guides from Lonely Planet.