She had a quick peek into the shop window.

Literal

She [topic-は] show-window [object-を] briefly peeked [tried-to-てみた].

ちょっと softens the action to 'a little, briefly' — it's not a full inspection. のぞく ('to peek, peer in') captures a glance through a narrow opening or into something one is curious about. ~てみる ('try doing') here marks the action as exploratory or tentative — not a committed look, just a casual check. ショーウインドウ is a katakana loanword for the display window of a shop, where merchants put their wares on view. Department-store ショーウインドウ in places like the Ginza became a Tokyo institution from the early 20th century onward, and the seasonal display windows of major stores still draw crowds.