From Diablo Wiki
Most Enhanced Damage Enchantments go by a range, between a low and a high number on a certain item. It will never always be the same, but of course, this only applies to all of the unique items on board up to v1.13 of Diablo 2 since magic items are varied by any trait. The Enhanced damage percentage applies to both Minimum and Maximum Damage on a Certain weapon, and the damage total depends on the min and max damage of the weapon and the percent enhancement. Like Mana Stolen Per Hit and Life Stolen Per Hit, the higher the min and max damage and the percent enhancement, the better. The Damage on the weapon will indicate a blue highlight when there is a damage enhancement applied onto it, showing a varied number. This damage can be stacked up with Damage to Undead and Damage to Demons but it only stacks when your attacks are directed at those selected enemies. Maximum Damage and Minimum Damage enhancements permanently stack upon your enhanced damage.
Enhanced Damage is useful for any weapon that can deal plenty of damage. wands and staffs aren't so suggested for this, but swords and axes make a great threesome when it comes to enhanced damage. There are plenty of weapons with this enhancement and the unique weapons have even greater enhanced damages as well.