In Darksiders II, you play as Death, one of the four riders of the apocalypse. You are trying to clear your brother, War, from his imprisonment based on accusations that he rode before the call was given to begin the "End War".
Darksiders II: Deathinitive Edition is the original Darksiders II game from Vigil Games and THQ re-released from publisher Nordic Games for current-generation systems (PS4/Xbox One), with polished graphics, reworked loot distribution and retuned combat. The re-release was performed by much of the original team now working as Gunfire Games.
The Deathinitive Edition contains all of the previous DLC integrated into the game (instead of clunkily dumped on you at the beginning).