There are three types of quests in the Quest Log: Kingdom Quests, Side Quests, and limited-time Event Quests.

Kingdom Quests appear with a golden background and progress your main storyline.
Side Quests are shorter side-stories for you to enjoy. These quests are not required to progress in the game.
Limited-time Event Quests have a unique background and are available during the duration of the limited-time event. Complete them while you can, since they are only available for the duration of the challenge!