Area of effect (often abbreviated AoE) is a term used to describe skills that affect multiple targets within an area.
Examples of AoE skills are the Ranger's Ice Arrow and the Elementor's Windfield.
Area of effect can also refer to non-combat skills. For example, Heal Rain may affect anyone within a certain range of the caster (but only if they are a member of the caster's party).
Since killing many monsters at once is obviously a fast way to level, virtually any job that has an AoE skill will have a build (or several) centered around leveling through use of it.