。
She raised three children on her own.
Literal
She [topic-は] alone [as-で] three-people [of-の] children [object-を] raised.
一人で here picks up an extra layer — 'as a single parent,' without a partner. The cultural weight in Japan is heavier than the English 'on her own' suggests: social systems and norms have historically presumed two-parent households, and シングルマザー (the loanword 'single mother') only entered mainstream discourse in recent decades. 三人の子供 puts the count via の; the counter 人 reads にん from three upward.