Leveling up will allow you to obtain characters to complete collections and earn various rewards. To do this, you will need to acquire crowns through Classic games, Tower Duel, Daily Challenge and Missions.
On the main screen of the game, you will see the level you are currently in, on the top left-hand corner, along with a blue star. On the same screen, you can see how many crowns you need to reach the next level, on the Epic Chest bar.
Note that as you level up, the amount of crowns needed to progress will increase.
We invite you to visit the article, What are the collections?, for more information.