。
She accidentally broke the vase.
Literal
She [topic-は] mistakenly vase [object-を] broke-and-ended-up.
誤って is the adverbial te-form of 誤る ('to err, make a mistake, be mistaken'), used as 'by mistake, accidentally.' Slightly more formal than the everyday 間違って. The accident is reinforced by ~てしまう (regret/completion auxiliary) on 壊す: 'broke it (and now it's done').' The compound 壊してしまった captures the cascading regret: action + finality + irretrievable loss. Note 壊す is the transitive ('break X'); the intransitive counterpart 壊れる ('break, get broken') would describe the vase breaking on its own.