The player level indicates how strong a character is.
To increase your level, you must gain EXP, which you can do by completing dungeons. Once you gain a certain amount, your level will increase.
Raising your player level increases the damage you deal to enemies, and reduces the damage you receive from them.
Each dungeon has a recommended player level.
The higher this rank is compared to your player rank, the more difficult it will be to complete the dungeon.