Upside-down means turned so that the top is now at the bottom. Inverted, and usually by accident.
The hyphenated form goes before a noun, so an upside-down cake or an upside-down map, and the unhyphenated version follows a verb. An upside-down cake is baked with the fruit at the bottom and turned out. There is a figurative sense about disorder, since an upside-down world is one where nothing works as it should, and children's books are full of them.
1adjectiveupside-downTurned so that the top is at the bottom.
“He was holding an upside-down map and looking confident.”
Middle English
up sid doun
English
upside down
English, today
upside-down
Built from
upside down comes from Middle English up sid doun, an alteration of earlier upsadowne, upsedowne, up-so-doun (“upside down”), equivalent to up + so + down.
Etymology from Wiktionary, CC BY-SA