The Quest icon changes depending on what you can do.

If you have a daily/weekly/monthly quest to claim it will show a treasure chest and the colour tells you which level - not sure which one it shows when you have different levels of quests to claim.

If you have any buildings under 21 it might show a building. If you haven't completed the t1-t3 troop quests it might show a troop type. If you have done all of those and just have knowledge quests it shows the sword and flag that you mention (used to show a woman). I'm not sure what happens once you complete all of the knowledge quests.