"Sie erschien des Nachts."
Übersetzung:She appeared at night.
There are a few more like the obvious "des Tag(e)s", "des Morgens". The most well-known is probably "Eines Tages" (one day,…). I think the adverbs "montags, dienstags, mittwochs,…" probably also are remnants of an old genitive construction. (Couldn't find a source, though. So take it with a grain of salt)
"Des Nachts" is a bit of on odd case since the true genitive would be "der Nacht" ("Nacht" is feminine"). It's just built in analogy to "des Tags".
Well, in other languages, some "weird" expressions that seem not to follow grammar are due to "hidden words", from a longer expression that was simplified.
(I just say it doesn't seem to follow Grammar because I really only know the very basics of it)
Perhaps the full expression could have been "im Zeitraum des Nachts" (I see that Nacht is feminine and this expression would be wrong anyway, but seems a locigal - but it doesn't make it true - explanation).