。
She did it out of curiosity.
Literal
She [topic-は] curiosity from did-so [explanatory-のだ].
そうした ('did so') uses そう as a pronoun-like proform standing in for a previously mentioned action — common in narrative when the action has just been described. ~のだ ('the explanation is...') gives the sentence the flavor of revealing motivation: 'the reason she did it is that it was out of curiosity.' Without のだ, the sentence would feel flatter, just stating a fact; with のだ, it provides explanatory closure. The whole structure is the typical 'why' frame for after-the-fact reasoning.