。
She loves gossip.
Literal
She [topic-は] gossip [subject-が] greatly-likes is.
大好き ('to love / really like') is 大 ('big') + 好き ('like') — a compound that intensifies a な-adjective without needing an adverb. The pattern Xが大好きだ is the standard way to express strong fondness for a thing or activity, parallel to plain ~が好き but with the upgrade in intensity built into the word itself. 噂話 specifically refers to gossip — chatter about other people, behind their backs — distinct from 噂 alone, which can also mean 'rumor' as a piece of information. The compound 噂 + 話 packages it as 'gossip-talk,' the social activity rather than the content.