。
She seems to have been happy when she was young.
Literal
She [topic-は] young days happy was [it seems-ようだ].
幸せだったようだ applies ~ようだ to a past state — the speaker infers from evidence that she was happy in her youth. 幸せ (しあわせ) is the standard word for happiness. The combination of a past-tense predicate with ようだ creates a retrospective inference — looking back and judging past emotional states from present vantage.