。
She has hundreds of books.
Literal
She [topic-は] hundreds-as-many-as books [object-を] is-having.
何百冊という is a useful intensifying frame: 何 + counter + という = 'as many as ~ / amounting to ~.' Compared to a plain 何百冊 ('several hundred volumes'), the addition of という adds rhetorical weight: it underscores the striking quantity. 冊 is the counter specifically for bound volumes — books, magazines, notebooks, and so on — pronounced さつ regardless of the preceding number. The whole sentence sketches a serious book-owning habit.