PvP stands for Player Versus Player as distinct from PvE or Player Versus Environment; that is, normal, storyline play against the AI. Some players find PvP thrilling and rewarding, and even go so far as to sacrifice PvE utility in their Character Builds to facilitate effectiveness in PvP.
In Dark Souls, PvP is accomplished by any given player using one of several online-only items to "invade" another player's world, or to lay down a challenge which another player can either accept or reject as seen fit. The specifics of the various methods of initiating PvP are detailed below.
source: Dark Souls wikidot PVP
In-Game-Description
Online play item. Invade another world. (Only Covenanter can use the item while Hollows cannot)
Defeat the master of the world you have invaded to acquire humanity.
The Darkwraiths of Kaathe use this orb to seek humanity and plunge further into dark. Perhaps they are more human than we?
Use
Allows for infinite invasions of other players You must be in Human form to use this item You have to be a member of the Darkwraith Covenant Depending on where it is used, the player will spawn at a corresponding spawn location.
Availability
It will be awarded to the player by Darkstalker Kaathe after joining the Darkwraith covenant and ranking up to +1
source:: Dark Sould wikidot Red Eye Orb