。
She went out for a walk.
Literal
She [topic-は] walk [for-に] went-out.
に here marks the purpose of the going-out — '[went out] for the purpose of a walk.' This 'purposive に' is the same に in 買い物に行く ('go shopping'), 食事に行く ('go to eat'), 旅行に行く ('go on a trip'). 出る ('go out, leave, emerge') is more compact and slightly more abrupt than 出かける ('go out, set off') — 出る emphasizes the moment of leaving, while 出かける emphasizes the broader excursion.