。
She was so kind that everyone liked her.
Literal
She [topic-は] very kind-was [because-ので] everyone [by-に] was-liked.
好かれる is the passive of 好く ('to like'), now somewhat dated in active form — bare 好く is uncommon in modern speech, but the passive 好かれる ('be liked by') stays in active use. The に here marks the agent of the passive — the entity doing the liking. Pairing the passive of preference with people-en-masse subjects gives the standard 'be popular' frame: みんなに好かれる, 子供に好かれる, etc.