Enhanced Damage is a magical property in Diablo II that is found on weapons. It grants a percentage-based boost to both the low-end and high-end damage amounts of a weapon. For example a weapon that did 10-20 damage that had +200% Enhanced Damage on it would effectively triple the damage of the weapon, boosting it to a 30-60 damage weapon. This modifier is found on many of the higher end weapons found in Diablo II.
Diablo III has an equivalent, "increased damage", that can appear randomly as a primary attribute on weapons. However, the bonus is only 6-10%.