。
She really loves cake.
Literal
She [topic-は] cake [subject-が] really-like [explanatory-んだ].
大好き ('love, very fond of') is the intensified form of 好き — literally 'big-like.' 好き / 大好き / 大大好き form a casual ladder of intensity in everyday speech. The clause-final ~んだ (the contracted casual ~のだ / ~のです) gives the sentence an explanatory or confiding tone — 'the thing is, she really loves cake.' Without んだ the bare 大好きだ would be more matter-of-fact; with んだ it sounds like the speaker is sharing a relevant fact about her, perhaps in answer to a question or to explain something else.