So, untranslatable means that there is no one-to-one correspondence between word a in language X with word b in language Y?

I think there is more to it than that. I think the article makes the point that Although the definitions seem fairly precise, the problem is trying to convey the local references associated with such words, says Jurga Zilinskiene, head of Today Translations, which carried out the survey

I can't think of any examples, but I know there are words in English that people who use it as a second language can use, but don't seem to really get all the nuances that a native speaker can understand.