Quests are special goals in the game that you can complete in order to get power-ups to help you progress in the game. The active quests and the current status can be seen all the time at the top of the game.
Complete quests and receive miles as reward. Collect and save up miles in your miles account. Spend miles in the Rewards section of the Quest Menu! If you complete the quests on time, they will give you more rewards!