Every language is built on a mountain of cultural context and assumptions. That's the part which is impossible to translate. You can translate the words but you're missing layers upon layers of subtle meaning.
Different scenarios require different methods of translation, sometimes you'll want something literal, and sometimes you can just translate the intent behind the words. As long as you can do that, I would consider it "translatable".
A paragraph footnote might accurately convey the intended meaning but it won't evoke the same feelings. A good author or translator cares about both these things.