The Power of Dominance is the Dark Lord's ability to absorb and control the souls of creatures that he kills. Known beings to possess this ability are Dracula, Alucard, Soma Cruz and Dmitrii Blinov (only because he copied it from Soma). The Soul Steal attack is very closely related to this ability, except that it involves killing the victim by stealing its soul (instead of stealing its soul after killing it), and the captured souls are immediately consumed for healing purposes, rather than being retained so that the bearer may call upon their power.
In Dawn of Sorrow, enemies must be killed in order for the soul to be stolen by Soma (since there are only a few souls available in the cellphone version of the game, enemies that contain souls emit green sparks when hit to distinguish them from those who do not). Once a soul is obtained, it must be first equipped before its powers can be used. Souls come in four types, based on how they are used: Bullet Souls, Guardian Souls, Enchanted Souls, and Special Ability Souls.
Dracula has never been seen using this ability other than in Portrait of Ruin, where he absorbed Death's soul to transform into True Dracula; although it's worth noting that he actually calls out loud the name of this spell as: "Soul Steal". Order of Ecclesia developed a similar ability involving the Dominus glyphs, which are based upon Dracula's power.