The Egg Balloon gives missions (ex: Destroy 13 Ballistas). Once you complete a mission, you get a certain amount of egg tokens. There are three mission slots: one where you can earn 20 tokens, one for 40, and another for 80. As you upgrade the Balloon, the there will be more and more tokens added on.
If you press the rhombus-shaped button (current event) once the page loads, you will see a bar to your left. The bar has four different sections: one for the current event, one for the milestones/goals for the event, one for the season (how you get divine dragons) and the last one for quests. There will be three quests.