Leveling Up is how you mark your progress through the game. It also allows you access additional slots! Progress is marked by experience points which can be seen by the Experience Bar. You can gain experience points to level up by betting.
The fastest way to gain experience is by betting high. For example if you bet $5 per line on 20 lines you may receive 100 experience for that spin. So in this case, it pays to bet big!
Leveling up has its advantages. When you level up you have more opportunities for extra coins, Bet Per Line increases.