(n.) a period of one night and one day
For such a fancy-sounding word, nychthemeron has quite a straightforward story to tell. Put simply, it is a period of twenty-four hours—that is, a period quite literally of one night and one day.
And at its root, etymologically, are just the Greek words for ‘night’ (nyks) and ‘day’ (hemera).
Something that lasts precisely one nychthemeron, incidentally, can be described as nuchthemerinal, or nycthemeral.
Why have such fancy words for something that simply means ‘one day’, or ‘lasting one day’? Well, back when these words were first dropped into use in English in the seventeenth century, there was a broader zeal for using classically-inspired words, and so something as impressively Greco-inspired as this would have fit that bill perfectly. That fondness for classical words has weakened in more recent decades, of course, but this word has clung onto existence in certain zoological, botanical and medical contexts, where having a formal word to describe something—like a blooming flower or a fever—that lasts precisely 24 hours proved useful.
Nowadays, you’re unlikely to find any of these words in use outside of these fairly esoteric contexts.