One of the two Primordial Serpents that the player can interact with. The other being Kingseeker Frampt. Darkstalker Kaathe is a lot trickier to meet and very easy to miss altogether. He is the head of the Darkwraith Covenant.
After you obtain the Lordvessel do not talk or interact with Kingseeker Frampt. Also, make sure you are not in the Princess Guard Covenant. If you are in the this covenant or talk Frampt, Darkstalker Kaathe will not appear.
After the defeat of the Four Kings, Darkstalker Kaathe will appear near a Bonfire and will tell you more of the story, from a different point of view. You no longer need to wear the Covenant of Artorias ring while in The Abyss.
Primordial Serpent concept drawing. There are two of these NPCs in the game that the player can interact with. Both will affect your game in different ways.