Borks papers are notes that Bork wrote and didn't include in the Book of Dragons. This was the only source of information aside from the Book of Dragons until the Dragon Eye was discovered. Hiccup received them on Bork Week in We Are Family, Part 1. The Dragon Riders often look to the papers whenever they need to find something really important.
When Berk was ready for Bork week, Stoick got Gobber to find his great-great grandfather's old notes, so they could give them to Hiccup. Hiccup was honored to be given Bork's dragon notes and learn the information that he hadn't put into the Dragon Manual. However Mildew had managed to place false dragon notes about Night Furies into one of Bork's notebooks, leading Hiccup to believe that they were real, until he and Toothless fell into a trap set by Alvin, his Outcasts, and Mildew.
Bork's Papers are often mentioned, usually by Fishlegs, when trying to search for information that he can't seem to find in the Dragon Manual. If any info is found, it's combined with any additional info possibly found in the Dragon Manual and/or the Dragon Eye, to create the most thorough collection of facts possible.
When they're seen, they're usually in an array of papers seen on Fishlegs' table in his hut, or on the table in the Edge Clubhouse while Fishlegs or Hiccup sort through them. They are however briefly seen in their compete bundle in "Snotlout Gets the Axe" while Ruffnut is attempting to rearrange Fishlegs' belongings due to them believing they are married.
In Secret of the Leviathan expansion pack, Fishlegs searches through Bork's Papers to find out about the Luminous Krayfin. He soon find that it is a 10 class Leviathan and must feed on the Dragon Bloom to evolve.
- Along with dragon info, Bork's papers also include Bork's fears, dreams, recipes, and even sketches of his neighbors, similar to a journal.