"everything or nothing"
Translation:всё или ничего
It's an idiomatic expression, so it's easier to just remember it as it is.
However if you want to deconstruct it, this sentence is about possessing/obtaining or not processing/obtaining something. In Russian when we negate existence ("there is no"), possession ("I don't have") or obtaining ("I don't get") of something we use the genitive case. Since Russian also uses the double negative, "ничего" would imply a negative sentence structure ("Нет ничего" as opposed to "есть ничто", the latter being ungrammatical), unlike English where the structure would be positive ("I have nothing" as opposed to "I don't have nothing"), intuitively native speakers use the genitive case with "nothing" even when "нет" is omitted.
нечто (nechto) - a less common synonym of что-то (chto-to) - something
ничего (nichego) - nothing
нечего (nechego) - something like a form of ничего (nichego) used only in phrases meaning "There is nothing". Мне нечего делать (Mne nechego delat') - There is nothing for me to do.