Jade Compendium is a book, written by Colloquo Votar.
In the books
In the A Song of Ice and Fire novels, the Jade Compendium was written by Colloquo Votar, and adventurer from Volantis. Many Maesters consider it the authoritative work (available to men in Westeros) on the lands around the Jade Sea.
The World of Ice and Fire (an in-universe history textbook by Maester Yandel) is primarily written from the perspective of an educated man in Westeros, with little knowledge of the lands east of the Dothraki and the Bone Mountains: only a brief outline is presented, with citations from the Jade Compendium, with "Yandel" (the author avatar) referring anyone who wants to know more about Qarth, Yi Ti, and beyond to read the full text of the Jade Compendium.
The Jade Compendium was first mentioned in the main novels, in the fourth book, after Stannis Baratheon arrives at Castle Black. Maester Aemon is skeptical of Melisandre's claims that Stannis is Azor Ahai reborn, so he asks Samwell Tarly to bring him a rare copy of it that he has kept in the castle's library. Samwell re-reads parts of it to the blind Aemon, including the detail that the sword Lightbringer is supposed to both glow and radiate heat - yet Stannis's sword "Lightbringer" (which Melisandre worked some magic on) only glows, not giving off heat. This seems to confirm Aemon's doubts about Stannis and Melisandre.
Aemon leaves the Wall with Samwell and Gilly in the novels on their voyage to Oldtown, though he dies in transit (in the TV version he died at Castle Black soon before they left). As he departs, Aemon tells Jon Snow that he left a book for him in his chambers with some important information he needs to know. By the fifth novel when Jon's storyline picks up again, he mentions that he read the copy of Jade Compendium that Aemon left for him, including the legends about Azor Ahai. As with Aemon, the detail that the real Lightbringer is supposed to radiate heat leads Jon to doubt that Stannis is really Azor Ahai reborn.