Intelligence is one of the five base attributes of characters in the game. For all classes, intelligence is the sole attribute that governs the total amount of mana the character will have. See the mana article for how this is calculated.
It is also the primary attribute for mages, meaning it is the attribute that increases attack damage for them. Therefore mages will have many more intelligence points than archers and warriors. Being the mage's primary attribute, it also increases hit chance for them by a small amount.
It's believed that intelligence also increases spell focus for mages, though this hasn't been confirmed; likewise it's also believed that it increases spell resistance for all classes.
Some special items of equipment will give bonuses to intelligence, including the Master Mage Amulet and Elite Mage Ring. Mages can also increase intelligence with the passive power Dragon's Blood, and archers with Wits.
Intelligence does not increase mana regeneration, as believed by some, at least not directly. See mana regeneration for more information.