Area Damage is an attribute in Diablo III that can be found on weapons, off-hand items, rings, amulets and shoulderpads. All slots except weapons roll up to 20%, while weapons can have up to 24% each.
It is measured in percent. With Area Damage, each successful hit made by characters or their pets (regardless of its Proc Coefficient) has a 20% chance to deliver additional damage inflicted to all enemies within 10 yards, not including the initial target. The severity of that damage depends on the damage of the base attack (which triggers the Area Damage in the first place), multiplied by Area Damage percentage. In other words, it is an effective DPS booster against multiple foes, designed to give players more flexibility in terms of attacking more than one enemy at a time even if they have only single-target attacks.
Against a single target, it gives no additional damage. Probably for this reason, Area Damage is not taken into account for the purpose of sheet DPS.
If the attack hits multiple foes, each of them will have a separate 20% chance to trigger Area Damage, damage based on the damage they sustained individually.
Up to 50% of Area Damage can be obtained from Paragon levels, as a choice of Utility tab, 1% per point, being the most damage-oriented stat from that category.
Maximum possible Area Damage one can get from items is 174% (plus another 25% from Demon's Hide, to a total of 199%). It can be stacked above 100%, being fully effective after that point: ironically, the enemies around the target will receive more damage than the target itself.
Attacks boosted by Area Damage do not have any special graphics, and do not even cause numbers to pop up; damage will be inflicted upon the targets without any special animation. This extra damage uses the same damage type, and will not trigger any special effects, including further Area Damage procs. Area Damage has a Proc Coefficient of zero and may not trigger any other special effects.
Note that channeled and damage over time spells calculate Area Damage as per tick, not per second.