"Pillaging will allow your forces to destroy furniture and tiles in an enemy dungeon. A player's starter dungeon can only ever be raided, not pillaged/conquered, but expansions are up for grabs. Creature have a pillage rating (viewable by hovering over a creature portrait on the creature panel) that show how capable said creatures are at pillaging. Ogres for example are slow, but very good pillagers."
The above description was taken from DO Developer 'TechOwl' on his post: 
You must launch a pillage attack from an expansion dungeon that can also be pillaged in retaliation. Therefore, it is not possible to pillage from your starter dungeon.