Draconite is a mythical stone, a gem of some kind, found buried deep within the still-living brain of a dragon. To obtain draconite, the brave hero must cut the gem free whilst the dragon is still alive, or the draconite will be useless, all traces of hardness having ebbed away with the dragon's strength. The time-honoured method of acquiring draconite, therefore, is to render the dragon somehow unconscious. Many stories feature herbs, either magical or otherwise, scattered about close to the beast and ensuring the deepest of slumbers, so deep that even having your skull cracked open and a gem dug out from the centre of your still-pulsing brain does nothing to disturb you. Of course, you could put the dragon to sleep and simply hack off its whole head; probably a more prudent course of action if you want to keep yours.
Draconite is hard; harder than diamond, even. Nothing can ever be carved or engraved into the surface of draconite, we're told, although it appears to be brittle enough to be chipped to form spears and arrows. Of course, in mythologies, such a gemstone was precious beyond words, and described as having magical and beneficial properties.
Pliny describes it as a white gem which drives away all poisonous animals and cures envenomed bites. It crops up in alchemical texts, and in English and Irish writings from the middle ages. There is a slight difference; these stories describe draconite as a mystical black gem, and there's little doubt that the gem being described is actually obsidian - among a range of Irish terms for draconite is the word obsianus, and it features strongly in the story of Mongan's death. Mongan, deserving of it or not, is struck by Arthur with draconite, an act which quickly results in Mongan's demise.
The idea of draconite is not merely part of Western myths, though; Chinese stories are big on dragons and precious stones, be it a pearl beneath the chin or the blue, lined object found in front of the dragon's horns in the Sun Kwang-hien. Finally, current usage of the word draconite, often as part of RPGs, extends to describing creatures which are half-dragon, an unknown metal of extreme hardness, and a stone formed from dragon's blood. It's easy to see how these have their origins in the draconite myth.