She thought back on her childhood.

Literal

She [topic-は] childhood [object-を] reminisced.

回想する ('to reminisce, to recall, to look back on') is a Sino-Japanese verb often used in literary contexts — memoir, novels, formal writing. 子供時代 ('childhood, child-time') is itself a compound: 子供 ('child') + 時代 ('era, period'). The same 時代 produces 学生時代 ('student era / school days'), 江戸時代 ('Edo period'). The whole sentence has a written, slightly literary feel — fitting an opening line of a novel or essay.