As some have figured out, Caim and the dragon are both the main characters of Drakengard. Although I have an avatar from the second game, let us assume that both are still keeping their appearances from the first game, with the dragon in her level 3 form (more explanation on that later)
Here's a general picture of the two
Warning Possible spoilers for the game of Drakengard
Caim
Species: Human, Male Age: 24
Caim was a soldier for a Union army in his olden land; in an effort to protect his younger sister from the forces of the evil Empire (that didn't end well). When in battle, he was terribly wounded and stumbling to the Union base castle he found something strange and terrible. A dragon, wounded and still retaining her pride. In desperation, the two created what is called (in their world) a "pact".
The two pulled their hearts/souls out of their beings and combined them, saving both their lives and starting powerful bond between the two. Should one of the two die, as well the other. Also, the human in a pact always loses something precious in the pact; with Caim, his voice. The two are able to communicate with one another from a mental link, but they have a tendency to stay close together. Caim mainly hates dragons, but keeps a softer spot for the red dragon, as the two rely upon one another to survive.
Caim's primary weapon is a sword (shown in the picture above) that belonged to his father, and it is able to shoot fireballs when enough energy is gathered within it. Caim is proficient in most weapons, but it is easily assumed that the sword is his prized possession. Also, Caim has superhuman strength, as per the pact, especially noted in his constitution, hardiness, and his breaking of the stereotype that white boys can't jump. Caim enjoys the thrill of battle, and is more than happy to have a giant freakin' dragon as a support. That firebreath, very soothing.
The Red Dragoness, Level 3 (Don't ask her true name, she won't tell. Caim knows, but he doesn't care to tell either)
head detail
Species: BFD (Big Fucking Dragon) Estimated Age: 10,000 years
As mentioned above, the dragon came into contact with Caim via the pact, and she has gained the chore of watching Caim/making sure the bloodthirsty idiot doesn't die. The two tried their best to fight for the side of the Union army, but all was for naught when Caim's sister perished. Caim, now lost and angry, had the dragon ferry him for his quest for revenge, and eventually ended up with him in this universe (by way of forces unknown).
The dragon herself does not care much for humans, but is fiercely loyal to Caim and will grudgingly help him in whatever form of trouble he gets himself into. She can come off as arrogant, but in the end, you will be very happy if she's on your side.
The dragon, having grown with Caim (and from the influence of the pact) has grown several times her original size, and gained much greater power than she could have attained on her own. She can launch 8 small homing fireballs, a single powerful fireball and, should she gather enough energy (it takes a while for it to charge), send forth a large magical blast comprised of many minuscule jets of flame. On their own, they don't do much, but the sheer number of fireballs is devastating.
Whew! Sorry for the wall of text guys.