。
She quit her job to take care of her children.
Literal
She [topic-は] children [genitive-の] care [object-を] do [purpose-ために] job [object-を] quit.
ために ('for the sake of, in order to') is the canonical purposive marker, attaching to a verb in dictionary form to express the reason behind an action. The pattern [verb dictionary] + ために + [main verb] is the workhorse 'in order to do X, did Y' construction in Japanese — slightly more deliberate than のに (purposive) and far more common in writing. 止める here is the standard verb for quitting a job (also written 辞める in this sense, with the kanji 辞 specifically reserved for resigning from work or office).