This page tells you about leveling up.
When you gain enough exp, you level up. You be given points, then you distribute the rest of them.
The higher the level, the stronger you'll be.
In Dokapon Games before The World
You can distribute 4, 5 or even 6 points. this is a great opportunity.
In the World
Points are automatically distributed, depending on your job.
In Kingdom
Points are distributed first depending on your job, before you distribute 2 of them.