。
She went out to buy food.
Literal
She [topic-は] food [object-を] buying [to-に] went-out.
出ていく (でていく) is a compound directional verb meaning 'to go out' — combining 出る ('to exit') with 行く ('to go'). The purpose-of-motion construction 買いに marks the reason for going out. 食べ物 (たべもの, 'food') is the everyday word for edible things.