The Dull Ember is a key item in Dark Souls II. It is the only ember available in the game.
When given to Blacksmith McDuff in The Lost Bastille, he will be able to modify weapons with the relevant stones. Unlike the original Dark Souls, only one non-standard Titanite stone is needed to modify a weapon; the item keeps its current upgrade level and is upgraded further with regular Titanite.
In Iron Keep, after lowering both ends of the bridge and while standing immediately in front of the fog door leading to the Smelter Demon, turn around. Jump over the gap (the chest here holds the Zweihander) and look to the right. Jump to that platform. The corpse hanging from the broken stairs is holding the Dull Ember.
Two iron chests will appear immediately in front of the player after they're transported from the Forest of Fallen Giants to the The Lost Bastille (after defeating The Pursuer). The chest on the right holds the Dull Ember.