Speed booking is the process of rapidly filling the minimum of pages in order to submit a storybook to the relevant NPCs. This is a commonly-used method of promotion-farming, reputation-farming, or Survivor power-leveling. Typically, you obtain several of the books and use teams designed to speed through each mission repeatedly. After each mission, you cycle the books until all have the same page filled in, the team adjusts builds (and perhaps heroes) for the next mission and follows the same process until the book can be turned in for reputation. In theory, if you are efficient enough at repeating missions, this accumulates reputation (and gold) faster than filling out an entire book.
 Young Heroes Trilogy
Young Heroes is relatively short and very simple, even in HM, since these are starter missions.
 Eye of the North
The most efficient use of speed booking is in Eye of the North, since you receive Hero's Handbooks with five pages already filled in; you need only complete three more. Typically, players add Against the Charr, Curse of the Nornbear, and A Time for Heroes (since those can usually be completed quickly).
A Speedbooker is someone who can solo these missions for other people; they are usually paid for their services.