Damage is any means by which unit's current health can be reduced. Heroes, creeps, items, spells and more are all capable of dealing damage.
Damage Sources
Damage is split into two primary types, Normal and Piercing. Unless otherwise stated, all damage is dealt as Normal Damage by default.
Normal Damage
Normal damage is assigned based on a calculation based on (Attack or Fixed Damage), Armor, and Health. The damage is initially calculated on your Attack or Damage stat, then reduced (or increased - if armor is negative) by the amount of armor that the target has and finally removed from their current health pool.
Piercing Damage
Piercing damage completely ignores all positive armor, and is dealt directly to the health pool of the target. Piercing damage is however amplified by negative armor, dealing increased damage as normal damage would.