Earning belts will help you process your journey and achieve levels. Level up to level 99 and through your journey, you will find Kira. Also you will be given tasks to get your belt.
Automatically, there is a scene where Clumsy Ninja stands up and pays attention. Then Sensei rewards your hard work with the belt. The ninja bounces around all happy. Normally you earn belts when you level up straight away. Certain levels unlock new belts, while others don't.
Unlocking belts follow a certain alternating pattern, where one level would have no belt, and the next level after that would have a belt. It goes on and on, except levels 39-50, where you can unlock belts at every level. This is possibly because the XP on levels 45-50 would require about 1 million or more XP to level up. There are belts beyond level 52, even stretching all the way to level 99, which means a lot more XP to grind.
At level 5 you will unlock Lily. At level 52, you'll unlock Kira.