Skyfire is a type of stone that made up the comet seen in The Brightest Night. When a dragon holds a piece of it, their minds and thoughts are shielded from being read by telepathic NightWings. For example, Moonwatcher and Darkstalker failed to read Turtle's and Onyx's mind since they carried a piece of the rock; instead, only being able to hear a low humming noise. If the skyfire rock is held in a mind-reading NightWing's talons, then the dragon cannot hear any others' thoughts, whether or not the mind they are trying to read is shielded by a piece.
Onyx claimed she found her piece when it fell out of the sky, burning a hole through her mother's head, killing her. Onyx called it skyfire, and kept the piece that killed her mother in an amulet worn around her neck. Turtle found a large piece that crashed into the ocean when he was swimming with some of his brothers. A few smaller pieces had broken off, and he had a jeweler make a golden armband to place them in.
Near the end of Moon Rising, Moonwatcher asked Turtle to take some pieces of the skyfire off of his bracelet, and she then gave the rocks to Qibli and Kinkajou as a gift so that she couldn't read their minds, and so they could keep their thoughts private.
In the beginning of Winter Turning, Moon told Turtle to give Winter one of the rocks, though he was doubtful.
In the second part of Escaping Peril, Moon explains that part of the reason she told Peril about her powers was that there was no way to give her skyfire.
At the end of Talons of Power, Turtle gives Anemone the fourth piece of skyfire on his armband.
Trivia
The rock "skyfire", is most likely referring to a meteorite known as tektite.
Skyfire is also the name of a video gaming team, which, coincidentally, has an emblem representing a dragon.File:Tektite.pngPieces of tektite, part of Crevs collection
It's possible that there actually is some sort of fire in skyfire because fire is able to temporarily stop Peril's mind from being read.
