。
She worked for her family.
Literal
She [topic-は] family [for-のために] worked.
A short, weighty sentence. のために marks the family as the beneficiary of her labor. In context this typically means working a paying job to support them financially — the implicit social model is one breadwinner taking on long hours so the rest of the household can be cared for. The bare past 働いた without further detail leaves it to the listener to fill in why or how, which is what gives the sentence its slightly poignant quality: it's a single line that could front a much longer story.