What does the Area Damage utility stat do?

Solution 1:

In your inventory>details>offense you can see statistic called Area Damage. Where it states :

"All attacks have a 20% chance to also deal X% of the damage to enemies within 10 yards"

Where X is "area damage" bonus gained from items and paragon levels(if skilled).

Each enemy that takes any damage from your hero,whether from aoe,DOT or single target spell/attack,will have 20% chance to deal X% of the damage it received in 10 yards radius around him. Making Area damage more effective when used with aoe spells on large groups. Source.

When triggered area damage instances can't crit on their own(no yellow numbers). However if you made critical strike on target that triggered area damage then it will splash X% of the critical damage you made.

There is also possible naming title bug on this stat which could cause some confusion.It says "Area Damage Chance : X%" where the title should be just "Area Damage : X%" . Because the chance is static 20% and they used damage variable X.

Here is an in-depth guide about area damage that was featured on official diablo 3 website.