。
She set off on a trip last week.
Literal
She [topic-は] last-week trip [for-に] departed.
出発する (しゅっぱつする) means 'to depart' or 'to set out' — a compound of 出 (go out) + 発 (launch/emit). The に after 旅行 marks the purpose or occasion of departure: 'departed for a trip.'