。
She bought one piece of clothing after another.
Literal
She [topic-は] one-after-another Western-clothes [object-を] bought.
次々に ('one after another, in succession') and the variant 次々と describe rapid serial actions — typical for shopping sprees, applause cascading through a crowd, dominoes falling, or any repeated event. 洋服 ('Western-style clothing') reflects a historical distinction maintained from the Meiji modernization: 洋服 (yōfuku, Western clothes) versus 和服 (wafuku, Japanese-style clothes like kimono and yukata). The split survives in vocabulary even though Western clothing has been the everyday default for over a century — a small linguistic fossil.