One way to see this word is a glass case with a small card beside it. Whatever you put in the case stops being an everyday thing and becomes something from another time, kept to be looked at. Both meanings of museum piece come from choosing what to put in the case: a hand-sewn dress, or your friend's phone with buttons on it.
可以想成一個玻璃展示櫃，旁邊還立著一張小小的說明卡。任何東西一被放進去，就不再是日常用品，而變成「別的年代留下來、拿來看的東西」。這個詞的兩個意思，差別只在你把什麼放進櫃子裡：手工縫的婚紗，還是你朋友那支按鍵手機。
From the word’s history
Wiktionary explains the compound as referring to the preservation of historic artifacts in museums; piece is the ordinary museum word for one single item on show.
維基詞典把這個複合詞解釋成「指博物館保存歷史文物的做法」。piece 就是博物館裡講「一件展品」的常用字。所以字面上的畫面，本來就是展示櫃裡那一件東西。
Wiktionary, "museum piece"
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