Definition:
The phrase "book up" means to reserve or arrange for all available places, tickets, or accommodations. When something is "fully booked," it means there are no more spots left because they have all been reserved.
While "book up" primarily refers to the act of reserving, it can also be used in a more informal way to mean to study or prepare thoroughly for something, particularly in a short time before an exam or event. - Example: "I need to book up for my final exams next week."
"Book up" is a useful phrase to know when planning travel, attending events, or anything that requires prior reservation.