Your ability to learn and remember facts and reason about events. Intelligence factors into the number of skill points you gain at each level. It is also important for some forms of spellcasting.
Intelligence is important for any character wishing to have access to a wide variety of skills. Skills are abilities not directly related to combat such as opening locks, placing traps, and crafting items. Intelligence is also absolutely vital for Mages, as it determines most of the factors related to their spellcasting.