A show 'Bible' is a reference document that television shows use to establish continuity, setting, character histories, the 'rules' of the world and other details. These pages of the I.P. Bible establish the premise of the pilot episode and beyond.
For example, the show Bible establishes certain facts such as "Animals do not talk in this world" and that the Water Tribes "have not been in contact in decades" and that "Fault line energies strengthen Earthbenders." Also, "When it is raining, Firebenders are less powerful." Fans almost never get to see this stuff, so prepare to squee out!
That said, these pages of the I.P. Bible also establishes the environment of the show. The section titled "Environment" says:
"This is an ancient, fantastical Asian environment, primarily Chinese. There are no modern things like electricity. However, the Fire Nation is in their industrial revolution. They use steam powered ships, lay tracks to move supplies."
- The A:TLA IP Bible
The I.P. Bible also insists on respect for source cultures from the very beginning, stating: "We generally do not show signs or writing in the show. If there needs to be a sign, it should be in Chinese with the proper translation, accompanied by subtitles." (As fans, we know that while signs did end up appearing every once in a while with shows, they were able to get away with not using subtitles by having characters read the signs or otherwise place the sign in context using dialogue.)
(And don't forget to check out the revamped Racebending.com!)