The game's story is about the waning Age of Fire which the player can help continue or end, the waning of the age also is the cause of the undead curse when Gwyn kindled the First Flame with his essence. Letting the Age of Fire end would bring about Age of Dark (a.k.a. Age of Humanity), but considering how Dark Souls (a.k.a. human souls) are prone to bad things and generally the world's bleak presentation of humans, this would probably be about as bad thing as the previous age or worse.
How bad humans and Dark Souls are or can be is especially shown in Artorias of the Abyss expansion (which is included in the Windows port of the game), though the information gained there can be somewhat misleading. The Abyss appeared because the pygmy went insane, not because it was natural thing to happen with Dark Souls, and the Abyss corrupted Artorias and the Oolacile. Many players seem to assume this is the natural progression for what happens with Dark Souls unfortunately.