。
She loves cats.
Literal
She [topic-は] cats [subject-が] greatly-fond-of is.
大好き ('really like, love' in a non-romantic sense) is the intensified form of 好き ('like'), built with the prefix 大 ('big, great'). The same prefix gives 大嫌い ('really dislike, hate'), 大事 ('important'), 大変 ('terrible, very'). Like 好き, 大好き is a na-adjective and takes the liked object with が rather than を — the canonical [topic は] [object が] 好きだ pattern of preference. For cats specifically, Japan has a deep cultural affection for them: 招き猫 (the 'beckoning cat' figurine), 猫カフェ (cat cafés, a Japanese invention), and 猫の日 (Cat Day, February 22, chosen for the にゃんにゃんにゃん pun on '2-2-2').