Vitality Damage, also known as Life Damage, is a type of direct damage, that affects a target's vitality to reduce it's health. Vitality Damage over time is called Vitality Decay. Both are reduced by Vitality Resistance.
Vitality Damage is effective against all types of 'living' monsters, including Beasts and Beastmen, Insectoids, Demons and Plants. Undead monsters and Constructs are 'immune' to this type of damage, though this 'immunity' can be broken using -xx% Vitality (Damage) Resistance or -xx% to All Resistances modifiers. Both the Spirit and Dream Mastery focus on using Vitality Damage as one of their main sources of damage.
Like the Elemental Damage types, Vitality Damage is affected by Intelligence and receives both a flat and a percentage bonus from it. The formula to this is the same that is used to calculate Elemental Damage output (Fire Damage, Cold Damage, Lightning Damage):
(elementalDamageDV * ((intelligenceDV / 650) + 1)) + (intelligenceDV*0.025)
This means, every 65 points in Intelligence increase Vitality Damage output by +10% and add an extra 1.625 points of flat Vitality Damage.
The special damage "+XX% Reduction to Enemy's Health" is also considered to be Vitality Damage and it's effect is reduced by Vitality Resistance as well. It doesn't receive any bonuses from Intelligence, though, and it's effect isn't increased by "+XX% Vitality Damage" modifiers.