Detailed Explanation
Demonic Soul permanently increases your damage as you get kills.
Each enemy kill gives you stacks, and each stack increases your damage by 0.1%.
With 1 copy, you gain 1 stack per kill and can store up to 1000 stacks, for a maximum of +100% damage.
Picking up additional copies does not reset your stacks. Existing stacks are kept, while new copies increase how fast you gain stacks and raise the maximum.