One way to picture 'uniquely': a long shelf of things, and one of them that has no twin anywhere on the shelf. Look along the row as far as you like and the match never turns up. Every use of the word starts from that search coming back empty — sometimes about how a thing was made, sometimes about where it is found, and sometimes about how far it goes.
From the word’s history
Wiktionary derives 'uniquely' from 'unique' + '-ly'. 'Unique' carries the idea of there being only one, and the adverb ending lets that idea describe how something is done, or how far it goes.
Wiktionary 說 uniquely 由 unique 加上 -ly 組成。unique 帶著「只有這一個」。加上副詞字尾之後，可以想成把「只有一個」這件事，拿去描述一樣東西怎麼做出來，或是一個程度走到多遠。
Wiktionary via kaikki (source_ref kaikki:3f6f69a190036ae4:1079355151:4709): "From unique + -ly."
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