。
She went out for a walk.
Literal
She [topic-は] walk [for-に] went-out-and-about.
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'). 出かける ('go out, set off, head out') emphasizes the broader excursion — a planned, often longer outing — distinct from the bare 出る ('go out, leave, emerge'), which emphasizes the moment of stepping outside. に出かける is the standard frame for any kind of outing: 買い物に出かける, 旅行に出かける, ハイキングに出かける.