The Mana stat determines the mana pool of your pet.
Mana is used whenever your pet uses an Ability/Move (such as Armor Ignore or Dragon Breath), or any Magical spell (such as Chivalry or Magery spells).
The higher the mana pool available to the pet, the more front-loaded damage it can produce.
Once the mana pool is depleted, the pet must rely upon their intelligence and Mana Regen stats to replenish the mana pool.
For longer fights where your pets mana pool has been depleted, your pet will cast abilities as it is able based on available mana that has been regenerated.