I couldn't get a reservation at the library. They were completely booked.
Why this joke works
Two Ways to Be Booked
A restaurant or event is “completely booked” when every reservation has been taken. A library is also literally full of books, so the same phrase describes both its schedule and its shelves. The setup works best as a mildly surprising complaint because libraries do not normally require reservations. Pause after the first sentence, then give the explanation with complete seriousness. The familiar booking phrase supplies the practical meaning first, while the location makes the literal book meaning unavoidable a moment later.
A closer look
A Reservation Problem Turns Inventory Into a Schedule
The first sentence applies restaurant or hotel language to a library, suggesting every appointment slot has been taken. “Completely booked” then explains the problem with both a full schedule and shelves full of books. The exaggeration is pleasing because being full of books is a library’s success, not a reason to reject visitors. The passive wording leaves an imagined librarian politely delivering the absurd refusal.
Fact behind the joke
A Library Catalog Describes Far More Than Books
The Library of Congress catalog contains over twenty million records for books, serials, manuscripts, maps, music, recordings, images, and electronic resources. Catalog records help identify and request materials and can include notes and circulation status. A library may have reservation systems for rooms or events, but “booked” is not a technical condition meaning every item in its collection prevents another visitor from entering.