An Area of Effect, or AoE, is a spell or ability that affects multiple targets within a pre-determined radius set by the game mechanics.
These effects can range from warlock DoT spells (such as Seed of Corruption) to wide area spells or warrior abilities such as Cleave. Traditionally, the primary target (also referred to as the anchor target or the focal point of the spell or effect) and those targets closest to it are the ones affected the majority of the AoE effect. Subsequent targets outside the immediate area are affected with diminishing returns as the spell or ability radiates outward from the source.
All area effect damage effects will have 'area damage caps' in patch 2.2.0 which limit the number of targets which will be affected by any AoE effects. There are already spells, such as Arcane Explosion (AE), using these to a certain extent. In the case of AE, the damage decreases per mob, up until about 15 mobs being, at which point it holds at a certain amount of minimum damage.
With GTAoE (short for Ground Targeted Area of Effect) spells, the player places a circle on the ground that will be the area of the spell effect, such as the Warlock spell Rain of Fire. He carefully places this around his targets and clicks to start casting/channeling.
All AoE healing spells differ from offensive AoEs, in that they only affect a limited number of players. There is no healing spell that actually affects all friendly targets in its area of effect.
Some AoE spells are used withthe caster as the anchor for the specific spell. The effect or damage radiates outward from the caster up to a specific range and affects all targets within that radius or the first targets the expanding "ring" or wave impacts. These spells are commonly referred to as "PBAoE" spells (short for Point Blank Area of Effect spells).