A Thestral Tail Hair is a hair taken from the tail of a Thestral and is used as a wand core. It is regarded as an unstable, if not the most difficult substance to use in wand making, though Veela hair is also described as such, but has been successfully utilised.
The most widely known wand to have used a Thestral tail hair is the Elder Wand. Created either by Death or Antioch Peverell, the Elder Wand was the strongest known wand in the entire history of wizardkind, and by legend was made to render the user invincible in wizard duels.
Whether this is a testament to the power of the Thestral tail hair remains ambiguous, as Elder Wand bearers, such as Gellert Grindelwald and Emeric the Evil, have been shown to be defeatable in a duel. Nevertheless, the Elder Wand has shown additional powers that other wands are not capable of, such as being able to successfully repair other wands, which was thought to be by people who have studied wandlore to be impossible.
It is assumed that one must be able to see Thestrals in order to utilise their hair, and since one must witness death first-hand to see a Thestral, anyone wishing to forge a wand with the hair must witness death, tying in with the story of being the "Master of Death." It is unknown if the tail hair would be invisible to a wandmaker who had not seen death, as a Thestral would be, or if it can be seen once it is separated from the Thestral.
- J. K. Rowling's official site (First mentioned)