The Japanese word for “compound” is jukugo:
熟語 (jukugo: compound) matured + language
Compounds typically contain two kanji. When they contain four, you have a yojijukugo:
四字熟語 (yojijukugo: four-character compound)
four + characters + matured + language
Most yojijukugo come from old Chinese poems, which told stories in four lines or four stanzas. The first served as an introduction, the second developed the premise, the third produced a climax or an unexpected change, and the fourth brought the story to a conclusion. The four characters in yojijukugo now represent those tales in a pithy way.
These compounds are considered idiomatic because the whole says something different from the sum of its parts. Therefore, a breakdown of the compound may not capture the meaning of any given saying.
You can find 3,300 such compounds at a website created by Kanji Haitani (who has a fortuitous given name). And of course JapanesePod101.com has a great series on yojijukugo.
