Quests in Fortuna is devided up in three categories: Growth Quests, Lord Quests and Prestige Quests.
Growth Quests are again devided up in two sub categories: Main Quests and Side Quests.
In the start, you'll get a lot of Growth Quests to help you getting started with the game and learn how things work.
Lord Quests are quests that require Action Power to activate. The higher the quest the higher the required Action Power.
For example: the Lord Quest: Pacify Rebels, require Lord level 40 and cost 1000 Action Power to start.
Each "level" of Lord Quests will have one that is influenced by your Military Points and one that is influenced by your Political Points.
Prestige Quests are quests where you gain Prestige and Hero Refresh Card by attacking NPC cities. The Higher the enemy city, the more Prestige.
You'll only get Prestige and Hero Refresh Card for the first 5 Prestige Quests every day.