。
She worked hard for her children.
Literal
She [topic-は] children of for-the-sake-of all-of-life-with-effort worked.
~のために ('for the sake of, for the benefit of') marks a beneficiary or purpose — 子供のために ('for the children'). 一生懸命 (literally 'with all of one's life') is a four-character compound (四字熟語 in spirit, though it's a productive expression rather than a classical proverb) meaning 'with all one's might, desperately, doing one's utmost.' One of the most culturally loaded adverbs in Japanese — 一生懸命に勉強する ('study hard') is the recurring exhortation to students.