There are many ways this could be explained, here are a few good story drivers that work:
Different areas have stronger and stronger enemies
Different areas in the world grow rougher and tougher as they stray from mainstream civilization. You can draw your party out into the wilderness for whatever quests they obtain.
A low level party would not be approached with a high level quest
A quest giver can easily size up the equipment and abilities of a level 2 party and see they aren't ready to face the ogre tribe he needs handled. Once the adventurers have made a reputation for themselves, they will be approached with more difficult work.
Include higher level content in the world that is being handled by someone else
The party could hear of a dragon being slain or fortress toppled - by a rival band of adventurers even.The higher level content they will one day do always existed, and in theory they could seek it out early, but for now it's just happening. Imagine in other places a quest would be happening ("slay the zombies and find out where they are coming from!") but the party just isn't there. ("The zombies kill a village, a small army is sent by the king to clear the source and takes heavy losses but succeeds")
Include lower level content at higher levels
Allow a leveled party to face a small goblin camp which can do nothing to stop their onslaught. It proves they have grown in strength, and allows players to feel strong in between the growing strength of enemies.
The party should have goals with more difficult methods
Find out what your party wants and open a path to it - then show that the path is blocked by harder and harder enemies. Present opportunities to the party that test their strength and reward their success. These opportunities will be increasingly strong in order to tempt an increasingly strong party, ans as such will be harder to obtain.
Or: Don't feel too much of a need to explain this
Finally - This is a problem which may simply not need solving. Like the in-story handwaving around how characters level up, the reasoning for them facing stronger and stronger enemies stems from it being a game. There is only so much you can do to hide the rules of the game behind a curtain.