Think of a line drawn round the lit stage. Inside it, the audience is looking; that is where the play happens. Offstage is the strip just outside that line, at the sides and behind: still inside the theatre, often only a step away, but out of everyone's view. Everything this word does comes from standing on the far side of that line.
The packet records the word simply as off + stage, which is the picture itself: away from the stage.
資料來源把這個字記成 off 加 stage，字面就是「離開舞台」，正好就是它的核心畫面。
Wiktionary etymology_text supplied in packet (kaikki:3f6f69a190036ae4:819810082): From off + stage.
Two branches
線外的位置：觀眾看不到的那一側
這一組就是核心畫面本身，只是分成「當副詞講位置」和「當形容詞修飾名詞」兩種用法。
r · B2
In the part of a theatre that is just beside or behind the stage, where the people watching cannot see. It says where a person stands or waits, or where a sound comes from, during a show.
在側台／幕後
線外的那個人：不表演時的生活
同一條線從空間搬到時間：台上他在演別人，跨出那條線之後，才是他自己的日子。
r · B2
At the times when a performer is not acting or performing, in their ordinary life away from the public.
私底下、下了台