She doesn't speak Japanese at home.

Literal

She [topic-は] home [at-では] Japanese [object-を] does-not-speak.

では layers the location marker で with the contrastive/topic は: 'at home (in particular/in contrast to elsewhere).' The implicit comparison here is loud — she may speak Japanese at school or work, but at home it's another language. This is a common scenario in households where one or both parents are non-Japanese, where bilingual children grow up navigating different languages in different domains. The verb しゃべる is conversational ('chat, talk') — slightly more casual than 話す.