AoE
Area of effect (often abbreviated AoE) is any ability that affects more than one target in a spherical area.
Mechanics
Targeting
There are two target types for area of effect abilities: personal and targeted. Personal AoE abilities (sometimes called "point blank") affect the area surrounding their caster (sometimes even targeting the caster themselves). Targeted AoE abilities require a target such as a player, a grave stone, or a building. Even if the target themselves cannot be affected by the AoE, their position in the world will be used as the center of the effect.
Target Cap
Most area of effect abilities have a limit to the number of targets they can affect. If the area in which the AoE is cast has more than this limit, a hidden roll is made to randomly choose from all eligible targets in the area to be affected.
The AoE target cap varies between abilities. This cap is usually listed in a power's tooltip.