AoE stands for Area of Effect and it means spells or abilities that affect a huge area usually damaging or effecting all opponents (or basically everyone except the caster/user) in that area. The classes most associated with AoE is the Mage class, with the specific Mage School usually being Invoker.

Mages are able to use weak AoE spells such as fireball to extremely strong ones such as chain lightning or even unleash chaos.
(though this is Mage School dependent)

Other classes that are able to use AoE:
>Clerics have a mix of AoE abilities, depending on whether a Priest or Paladin
>Fighters are said to be able to do AoE specials when using 2h swords
>Druids are able to cast AoE spells but are greatly restricted in where they can cast those spells
(thus greatly reducing their effectiveness)
e.g. a druid cannot cast landslide at the sheeps in Anshelm