Completing levels and quests gives you experience points. You can see how much experience you’ll be given for each level on the ribbon at the top of the level selection window. For quests, you will find out how much experience you have received in the “Rewards” window after completing the quest.
Once you obtain a certain number of experience points, your experience level will increase. This increases your maximum energy level, fully restores your energy, and may give you additional items.
Your experience level is tracked in the upper-left corner of the world map screen. Tapping the indicator will show you how many points you still need to obtain to reach the next experience level.