Every player has a level associated to their character. When a player starts off as a Visitor, their initial level is 1.
As the player kills monsters and completes quests, they receive EXP. After obtaining a sufficient amount of EXP, they level up. The amount of EXP required to level increases exponentially (view EXP Chart) as the player gains levels: basically, low-level players don't need a lot of EXP to level while high-level players need a huge amount of EXP. Fortunately, monsters around the player's level tend to give fair amounts of EXP, making it fairly easy to level up!
Level 230 is the current maximum level.