Level is a game play mechanic for balance reasons to and determine the proper challenge for a player or group of players. Even if the monsters are stronger in a new zone or expansion, it does denote the level of danger but overall level is simply a mechanic for players and designers to know how strong and capable their characters are.

Lore wise our heroes are very capable people no matter the level, though often the scope is tied to the level of the threat where at low levels we are dealing with issues that affect just a single city-state to more global concerns at level 50+, if anything the biggest tie between level and lore is the scope of our actions and their impact on the world.

Level 1 we are nobodies, level 10-15 we are recognized local adventurers of skill, by 30 we are local heroes of Eorzea, by 50 we are renowned champions that have a great deal of influence and I expect by 60 we will be big damn heroes hose very presence will influence grand events just like the end of 2.55. But ultimately level is just a gameplay mechanic.