Think of a line drawn on the floor of an airport. Goods that cross that line into a country normally have a tax added to them, and the price goes up. Duty-free is the small opening in that rule: the tax has simply been left off, so the same bottle costs less on this side of the line than it will on the other. Everything the word does grows out of that missing tax — the goods it is missing from, the bag you carry them home in, and the shop that is allowed to sell them that way.
From the word’s history
Wiktionary analyses the word as duty plus the suffix -free. Duty is the tax charged on goods entering a country, and -free means without, as in tax-free or sugar-free. So the word says, in its own parts, that the tax has been left off.
Wiktionary 把這個字拆成 duty 加上字尾 -free。duty 在這裡指貨物進入一個國家時要繳的稅。-free 是「沒有、免掉」，跟 tax-free、sugar-free 的 -free 一樣。所以這個字的組成本身就說出了核心畫面：那筆稅沒有被加上去。
Wiktionary entry for duty-free (packet source_ref kaikki:3f6f69a190036ae4:1328602987:11915): From duty + -free.
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