You can picture something turning fast, and a piece leaving it. The piece is not thrown away — it lands, stays whole, and starts moving on its own. Two details carry all three meanings. The piece began as part of something bigger, and it now has a life of its own. Whether the piece is a side character, a department of a company, or a useful result nobody planned for, the same thing has happened: it came off the main turning body and kept going.
From the word’s history
The noun comes from the phrasal verb spin off. The verb is the movement; the noun is the piece that came off.
這個名詞是從動詞片語 spin off 變過來的（來源寫的是 deverbal from spin off）。動詞講的是「甩出去」這個動作，名詞指的是「被甩出去的那一塊」。所以英文寫法也分家了：動詞是兩個字的 spin off，名詞才是 spin-off。
Wiktionary entry supplied in this packet (source_ref kaikki:3f6f69a190036ae4:1387417151): 「Deverbal from spin off.」
登入就可以看每一支怎麼連回核心畫面。