Black wool is obtained during the Sheep Shearer quest from Black sheep. Previously, ordinary wool was used to complete this quest, but instead has been replaced with this quest-only item as of 15 December 2009.
Before the 15 December 2009 update, players would normally click on a white sheep and shear its wool. Unfortunately, the player may accidently click on a ram. This would accidently attack it. As most players who started Sheep Shearer were lower levels and new to the game, the rams could lower the player's Life Points and could easily die. Now it is harder to make that mistake as you should only be seeking black sheep.
Black wool can be used on a Spinning wheel to make a ball of black wool.
Upon completion of the quest, player may no longer use shears on the black sheep to obtain this form of wool, and any wool in your inventory or stored in a bank is removed (presumably by Fred).