She went to that market once a week.

Literal

She [topic-は] week [per-に] once that market [to-へ] went.

市場 (いちば or しじょう) means market — いちば for a physical marketplace, しじょう for an abstract market (stock market, etc.). Here it refers to a physical market she visited regularly. The past tense 行った combined with the frequency expression 週に1回 indicates this was a past habit that may no longer continue.