Throughout the history of the Castlevania series, the exact nature of Dracula's power was never clearly established. Early games just allowed you to assume that he was a vampire and all vampires were simply that powerful, but as the games trended on, and other vampires were introduced (Carmilla, Elizabeth Bartley, Actrise, among others), an explanation for why he was the head of the this whole clan was needed. Was it simply that he was the eldest and thus the most powerful, or was there another explanation?
Eventually, two games more fully fleshed out the exact nature of Dracula's power. Castlevania: Lament of Innocence established that there were two stones -- the Ebony Stone and the Crimson Stone -- that gave the vampire who wielded the immense power and abilities. But where did these stone derive their power? Where did Dracula go when he died and where did his castle, a creature of chaos that ever-changed, come from? For that answer we had to look one game earlier, Castlevania: Aria of Sorrow. Here it's established that Dracula's power comes from a place called the Chaos Realm, the extra-dimensional source of the evil magic that charged his magic and created his evil abode.
The fully eliminate Dracula you couldn't simply kill him because, as shown time and again, his soul could be resurrected (sometimes in the same body, other times in new hosts). No, to really destroy Dracula you had to not only seal away his power (as the heroes tried in 1999 AD) you had to go to the source, to the Chaos Realm, and kill the personification of that power: the demon Chaos.
That's exactly what hero Soma Cruz (the reincarnated soul of Dracula, now in the body of a good person) did in Aria of Sorrow. After learning his true nature and discovering his demonic powers, Soma chose to venture into the heart of the castle, to the Chaos Realm, to take on Chaos and end the possibility of Dracula ever coming back in his evil form again. Dracula's true power was destroyed, and all that was left was to watch the castle crumble one last time (at least until Castlevania: Dawn of Sorrow complicated matters).
Fighting Against Chaos:
At the start of the battle with Chaos the demon will drain all your collected souls out of you. This will depower you, for a time, and leave you with just your weapons to use in your attacks. Your souls will be trapped in three orbs (blue, red, and yellow to correspond to most of the souls you've collected) that will slowly rotate around the demon and you'll have to attack each of these repeatedly until they break, releasing each group of souls that was stolen from you. Watch out, though, as each of these crystals will fight back in turn: yellow will shoot out a large blue reticule at you dealing touch damage, blue will similarly shoot out a demonic/angelic form at you to deal touch damage, and red will summon three crystals that will shoot at you.
Once the crystals are defeated, and your souls are all regained, the true core of the demon will be revealed. It can attack you in a few ways. One is to shoot a skull dragon at you, which will snake its way around the screen dealing touch damage. The core can create a circle of spikes that will shoot out in a spiral pattern. The demon can also summon a larger green orb that will bounce quickly around the screen, and smaller orbs that will slowly home in on Soma. This can all combine to deal a lot of damage. The goal here is to kill the four eyes in the corners of the screen. This will then made the center of the demon more susceptable to damage (each eye killed allows for more damage to get through). It's easy to soak a ton of damage here, but just keep wailing away on the center as much as you can and eventually you'll bring the beast down.