Area of Effect (AoE) means an effect (often damage, but also buffs and debuffs) that affects multiple targets within an area or radius instead of a single target. AoE damage is also known as splash damage.
Certain weapons and abilities in Dawn of War and Dawn of War II have an AoE, which is often a circle area but may also be line- or wedge-shaped. Weapons that deal AoE damage include flamers and analogues (e.g. sonic blaster), grenades and other explosives, and artillery weapons such as the prism cannon of the Fire Prism tank. Many abilities have an AoE effect that may be either targeted or centered on the performing unit. These may also have a DoT (Damage over Time) effect.
AoE attacks typically deal low damage but affect numerous models or units at once, so they are generally devastating to clumped-together low-health units (light infantry) but less effective against highly durable single targets.