The Dark Soul was a unique Lord Soul claimed by the Furtive Pygmy, the presumed ancestor of the Chosen Undead. Passing the Dark Soul down through its descendants, it hoped that one day the Dark Lord would be born amongst them to extinguish the Age of Fire, bringing about the Age of Dark.
Some sources also suggest that the Dark Soul has since been split. Much in the same way that Gwyn split his own soul into fragments and gifted them to Seath the Scaleless and the Four Kings, although to a much greater extent. This being the case, it is theorized that Humanity itself comprises the shards of the Dark Soul.
It is discovered that the Dark Soul carries the power necessary to create a painted world, and the Painter of the next incarnation uses this "pigment" to paint a cold dark world on a canvas to revitalize the current painted world, once two Unkindled arrive and ignite the flame that burns rot away.