The Carn Dum Captain, obviously, is the captain of the fortress Carn Dum. He is most likely the commander or lord of the barbaric people of Carn Dum. The Captain is likely a strong follower of Agandaur. His ancestors (or himself, depending on if his sorcery can prevent aging, like Black Numernoreans) probably served the Witch-King when he came North to conquer Arnor. He, or his ancestors, led the barbaric race of men against Arnor alongside the Witch-King. Either the Witch-King tought him sorcery when he joined forces with him (again, if he is akin to the Black Numenoreans), or Agandaur taught him sorcery when he journeyed North. It is most likely he is akin to the Black Numenoreans, as he posseses powerful sorcery powers. Agandaur travelled North probably only a few days/weeks before the Nazgul attack on Sarn Ford. This is not enough time to master the dark arts. Wulfrun, Agandaur's prime follower, is a master, but he was under Sauron's and Agandaur's sway for a very long time. Other orc and goblin shamans used the scrolls forged by Agandaur, but couldn't relocate themselves or do great damage with the dark arts like Wulfrun, the Captain or Wuflrun. So, it could be thought that the Captain is akin to the Black Numenoreans.
When Agandaur travelled to Urgost's lair to attempt to join forces with him, he brought with him a contigent of the Barbaric Men of Carn Dum, and their Captain, The Carn Dum Captain of course. When the dragon, Urgost, hesitated to join forces, and had to think about his descision, Agandaur left to "prepare" his reward (he put a siege on Nordinbad, as Nordinbad was the dragon's reward). But when he left, he didn't want to have no one around when the dragon made up his mind, so he left many of the Barbarians and the Carn Dum Captain to awit the dragon's descision. But they wouldn't last long enough to hear his descision, as the Fellowship of the North arrived to try and slay the dragon before he could ally with Agandaur. The Carn Dum Captain as his guard set up camp on the dragon's very doorstep. When the Fellowship showed up, the Captain readied his powerfull sorcery, which could easily match or even prove better than the Lore-master Andriel's power. But the combined power of the Fellowship proved better than the Captain's, even though the Captain's powerfull strength with his staff proved unblockable, and with his sorcery, he would flee to a higher point of elevation and pound them with sorcery. But that wasn't enough to stop the Fellowship, and they soon brought him to his knees, saying him on the dragon's doorstep.
It is also good to note that The Captain of Carn Dum held one of the seven scrolls belonging to The Cult of the Lidless Eye.