You can think of the whole word as one small sticky strip pressed over a cut. It takes two seconds. It hides the sore place and keeps the dirt out. And the cut itself is still there, unchanged, under the pad. Everything this word does comes from that: sometimes you are talking about the strip, sometimes about the act of pressing it on, and sometimes the sore place is not a cut at all but a problem at work.
From the word’s history
Wiktionary records Band-Aid as a trademark registered and coined by Johnson & Johnson in 1924, built as band(age) + aid, and now used as an ordinary word.
維基詞典記載，Band-Aid 是嬌生公司在 1924 年註冊並創造的商標，由 band(age)（繃帶）加 aid（幫助）組成，後來變成大家通用的普通名詞。所以字面上本來就是「幫一下忙的小繃帶」，短短一片，份量本來就不大。
Wiktionary (kaikki extract kaikki:3f6f69a190036ae4:1178333804) entry 'band-aid': 'Genericized trademark from Band-Aid, registered and coined by Johnson & Johnson in 1924 as band(age) + aid.'
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