Bane is an item property introduced with Publish 83. For a chance to trigger this on hit effect, the target's health has to drop below 50% first. The far, the better is the chance. While at the same time the additional damage caused grows up. Starting with about 50% of its damage potential at targets half life, growing to 100% near targets death. The additional damage caused is 30% of targets Max. HP capped at 350 physical damage - before damage reduction by physical resist.
Example PvM (by Bleak on Stratics):
Baracoon's maximum hitpoints : 12,000 HP
30% of 12,000 is 3600 physical damage from bane but is capped at 350 physical damage.
350 physical damage - 70% physical resist of Baracoon = 105 damage
At half health the proc in this case will start at 52 damage and will scale up to 105 damage as the mob loses life.
Character's maximum hitpoint: 150 HP
30% of 150 is 45 physical damage from bane
45 physical damage - 70% physical resist of the Character = 13.5 damage (subject to unknown rounding rule)
At half health the proc in this case will start at 7 damage and will scale up to 13.5 damage as the character loses life.
Runic Crafting, Reforging & Imbuing
As of today (2017-09), Bane is a property only available on Ararat Artifacts and weapons from the invasions of the Shattered Obelisk event cycle. It is not possible to runic craft or reforge items with the Bane property nor to imbue it onto items.