When a language is only taught from the adults that speak it. I know there's a word for it, but I can't for the life of me remember what it is!
The common term for the languages only taught from the adults that speak it is mother-tongue. Google defines mother-tongue as :
the language which a person has grown up speaking from early childhood.
You can also use natal tongue, native tongue, parent language.
From your question's title "Passed down language?" and from the descriptive part of your question, "When a language is only taught from the adults that speak it.", I take it that you are asking for the label given to languages which are passed on with little or no written form.
Consider the term orality. According to the linked page, primary orality (or primary oral culture) relates to cultures with no writing or print, and secondary orality (or residual oral culture) relates to cultures where many don't use writing even though it exists.
Have a look also at the term oral tradition, which refers to cultural knowledge passed on orally (presumably, even if writing was available to the society at large).
If you mean the language that is taught by mothers and fathers to their children at home, as opposed to a formal language taught in schools, etc, then it would normally be referred to as the "local" language, or the "native" language, depending on the specific circumstances.
A set of terms are used interchangably to refer to what I suppose you're asking about, which is
a first language, arterial language or cradle tongue.
The terms often used interchangably with 'first language', 'arterial language' and 'cradle tongue' are those mentioned in previous answers:
- mother tongue or mother language
- native tongue or native language
One problem with using these terms interchangably is that, in some cases, the mother or native language is not the first language of a child. The 'mother tongue' or 'native language' is, rather, the language common for people of the child's ethnicity. Children may not ever learn their mother tongue.
first language n. the language which a person first acquires in infancy, usu. in contrast with another acquired subsequently
["first, adj., adv., and n.2". OED Online. September 2015. Oxford University Press. http://www.oed.com/view/Entry/70609?redirectedFrom=first+language (accessed November 25, 2015).]
refers more precisely to the first language learned from adults by children too young to read or undertake formal instruction.
Other potential problems with using the terms interchangably include those suggested in this quote from David Crystal as cited at the "native language (L1)" entry in the "Glossary of Grammatical and Rhetorical Terms" at about.com:
As David Crystal has observed, the term native language (like native speaker) "has become a sensitive one in those parts of the world where native has developed demeaning connotations" (Dictionary of Linguistics and Phonetics). The term is avoided by some specialists in World English and New Englishes.
In an attempt to sidestep problems,
Contemporary linguists and educators commonly use the term L1 to refer to a first or native language, and the term L2 to refer to a second language or a foreign language that's being studied.
Such efforts to sidestep problems fail, as likewise all the terms so far discussed fail to describe, the not uncommon situation wherein children learn their first languages in truly bilingual households from bilingual adults.
If aren't looking for oral tradition, maybe you are thinking of "culture." Cultural heritage is all the knowledge that is passed from one generation to the next. The phrase doesn't focus completely on language, but I feel it addresses the question.
See the following address for a detailed description.