Dark Lord Candidates are individuals who were born on the exact time of Dracula's permanent demise caused by a solar eclipse on the Battle of 1999. These individuals would develop unique powers, each of which seems to be inherited from the powers of Dracula. Each one is valid to become the next Dark Lord if certain circumstances are met.
Every time Dracula is slain, he is reborn in order to balance the good of God with the evil of the Dark Lord. The Dark Lord candidates are children born at the same time of the Dark Lord's demise, inheriting a sample of Dracula's power. In Castlevania: Dawn of Sorrow, the cult leader of With Light, Celia, believes candidates can inherit the Dark Lord's true power and become the rightful King of Darkness. To do this, they must slay the one who possess the soul of Dracula and claim the throne of Dracula's castle; along with this comes the power of Chaos. Although Graham Jones technically wasn't a formal Dark Lord Candidate, his status regarding inheriting some magical abilities and being born the second Dracula was killed nonetheless inspired Celia to find similar individuals.
At the end of Dawn of Sorrow, Soma and probably Dario are the only ones still alive, making them the only known Dark Lord candidates in 2036, although the latter was stripped of his pyrokinetic abilities.