Completing Campaign quests progresses the story.
If your current power level is below a quest's recommended power, you will deal reduced damage to enemies and take additional damage from their attacks. Keep your gear updated to ensure you have the strongest possible loadout before embarking on a quest.

As the story progresses, various actions/features/quests are unlocked.

After Completing Palace of Web

• Feature Unlocked: Recycle
• Feature Unlocked: Craft

After Completing Dragon's Lair

• Accessories: Slot Unlocked

After Completing Emeslam, Temple of the Sun

• Feature Unlocked: Gideon's Coffin Customization
• Action Unlocked: Dynamis Abilities

After Completing Zababa's Bailey

• Feature Unlocked: Orders
• Content Unlocked: Skirmishes

After Completing Skyborne Pantheon

• Feature Unlocked: Meld

After Completing Epsilon VII

• Accessories: Slot Unlocked

After Completing Heart of the Blue Sun

• Content Unlocked: Sieges
• Feature Unlocked: Gideon's Coffin Voice Customization
• Feature Unlocked: Enhance