Think of a cat crossing a wall: the path is barely a hand wide, it is high above the ground, and the cat walks it without a wobble. A catwalk is a path built like that for people — long, narrow, raised, one person wide, with everything else far below. Under a bridge or above a theatre stage it stays exactly that, a working path to somewhere you could not otherwise reach. In a fashion show the same strip is kept but the purpose flips: now the height and the narrowness are there so that everyone can see the person on it.
From the word’s history
Wiktionary gives the word as cat + walk — a path of the kind a cat can manage. That reading sits under the narrow raised walkway directly, and the fashion stage borrows the same shape.
Wiktionary 把這個字拆成 cat（貓）+ walk（走道），也就是「貓走得過的那種路」。這個拆法直接對上高處窄道的意思，而時裝秀的台子只是借用了同一個形狀。
Wiktionary, entry 'catwalk' (kaikki extract, source_ref kaikki:3f6f69a190036ae4:1256899619): 'From cat + walk.'
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