In the "Quests" you will become familiar with the basic game mechanics and learn to use them. Quests also tell you the story of Witchcraft world and why this world needs you.
At the "Quests" page the game offers you a set of different tasks (brew a potion, defeat a monster, upgrade an item, etc.). Complete a task to get a reward. You can only do one task at a time. The next task becomes available when you complete the previous task and collect the reward.
Quests are split into chapters containing 4 quests each. Starting from chapter 21 you can skip a quest if you don't want to complete it. Please note that it costs gems. If you skip a quest using gems you still get the rewards for it.