Campaign quests are those that must be completed in order to progress the story.
Although not tied to story progression, completing Skirmish quests can yield generous amounts of crafting materials and Relics.
Additionally, each Skirmish you undertake has a chance to bring you face-to-face with Infamous enemies.
Sieges are challenging quests which test your mettle in a variety of different battle situations.
Each Siege completed will reward you with Signatums which can be used to purchase a variety of rewards at the Exchange, including crafting Blueprints for extremely powerful items.
Sieges are updated on a weekly basis, and each Siege is themed after a specific element. Making sure your loadout matches the elemental theme of a Siege is paramount to success.