She lives in a big house.

Literal

She [topic-は] wide house [in-に] is-living.

広い ('wide, spacious, broad') applied to a house translates as 'spacious' or 'big' — Japanese houses, especially in urban areas, are notoriously compact, so 広い家 carries a small note of admiration or aspiration. The countryside (田舎) often offers more 広い houses, while Tokyo apartments rarely earn the label. 住んでいる takes に for the place of residence — に for existence, never で.