The Noki Bay book or secret book is an oddly placed object found in the mission Red Coins in a Bottle in Super Mario Sunshine. The book is placed inside a rock formation at the bottom of the titular bottle, behind a door that does not open.
Glitches allow both Mario and the camera to clip inside these rocks and view the "secret" book. Consequently, the entire structure's unclear purpose, and appearance of being cut content, has become a source of rumors and speculation. Details from the theories and rumors below have often been treated as fact online.
Theories
The standard speculation is that an early version of the game had a mission where Mario would retrieve the book and bring it to the Noki Elder for a Shine Sprite. Hacking to reach the book reveals that it has no collision and cannot be interacted with.
Sources related to this theory often claim that this early mission was replaced with the Red Coin mission present in the final game. According to The Easter Egg Archive and a "Glitchtopia" wiki article on the subject, "some people" believe that this change was made between the Japanese and international versions of the game. Sources such as the Super Mario Wiki fail to substantiate this claim.
Miyamoto's "door to another world"
Theories have claimed a recurring connection between Mario creator Shigeru Miyamoto and the Noki Bay book. For instance, IGN forum users drew parallels to the following inspirational quote attributed to Miyamoto in the Nintendo Power magazine.
What if everything that you see, is more than what you see? …the space that appears empty is a door to another world? What if something appears that shouldn't? You either dismiss it or accept that there is more to the world than you think. Perhaps it is really a doorway, and if you choose to go inside, you'll find many unexpected things.
In this situation, the thing to appear through the otherworldly door would be the secret book, and pursuing it would lead to further secrets.
Miyamoto's quotes have previously hinted at features in upcoming games, such as the Metal Cap in Super Mario 64. However, this quote has a seemingly figurative connection to the book that it supposedly hints at. The door in question is decidedly mundane, and cannot be passed through by intentional means.
If this was ever meant to hint at the book, then the access the quote describes was patched out later in the development of Super Mario Sunshine. This much isn't an entirely unreasonable conclusion, as a lot of content had to be cut from the game before release, including several worlds.
You have no life
The textures of the book are similarly rumored to include a message from Miyamoto, written in Japanese, telling the viewer that they are wasting their time for bothering to read its contents. The traditional "loose translation" reads as follows.
You have no life. Signed, Shigeru Miyamoto
Though this sounds fabricated due to the uncharacteristically insulting tone of the message, textures relevant to the book don't appear to be easily accessible online. Definitively confirming or debunking this rumor requires more research.