Tenebrium is black rock appearing in Divinity: Original Sin.
The first point of Tenebrium allows a character to safely handle any Tenebrium in any state without contracting the worst disease in the game,Rot1 non-leathal Void Damage per Turn . You can get the first point of Tenebrium ability by clearing the quest given by Brandon at Silverglen, or reading a book at the Geomancer's house at Sacred Stone.
Tenebrium ability increases a character's damage when using Tenebrium weapons of any variety. Each point increases damage by 10%. Theoretically, Tenebrium ability can reach up to 10 points.
Tenebrium weapons are the same as their normal metal or wooden counterparts, but do more damage. Also, it seems that you cannot improve Tenebrium weapons on a sharpening wheel.