Pre-Hardmode is the initial state of the player's world.
It is essentially an 'easy' version of the world, featuring enemies and items appropriate for new characters. Pre-Hardmode begins at world creation and ends with the defeat of the Wall of Flesh. Defeating the Wall of Flesh will irreversibly turn the world to Hardmode which adds more content and makes the game more difficult.
This is part of systematic game advancement.
The term "Pre-Hardmode" refers both to the Pre-Hardmode world itself and to content accessible in Pre-Hardmode worlds.
There is little reason to keep a world Pre-Hardmode as Hardmode does not remove Pre-Hardmode content (with a few exceptions).
Reasons for postponing Hardmode include having an easier game experience, or to make extra preparations (such as building Houses secure against enemies, or digging tunnels to protect biomes) before Hardmode begins.
