The Dragons are an ancient species in the Supernatural universe and had been known to ancient hunters and other humans.
Dragons have existed as long as humanity, and maybe before. They are one of the strongest of the supernatural monsters, and have eluded detection for centuries, a feat considering their giant size. Indeed, it is possible that King Arthur, in universe, was a Hunter of supernatural creatures, and hunted the Dragons to save humanity. The Dragons have never been seen in their true forms apart from large dark shadows with wings, but have been shown to be larger than a small aircraft, and to be able to keep up with the speed of a small plane. The Dragons were given the ability to shape-shift by their Mother, Eve, who planned to conquer humanity. The Dragons had been hunted almost to extinction, but like all other supernatural monsters they went to Purgatory upon their deaths. So in modern times, most humans and even most Hunters believed them to be a myth.
In the show
In season 6, the episode Like A Virgin centered around Dragons and their love of female virgins. Dean noticed some monster had been abducting virgins and he wondered why, given that he preferred women with "experience." Sam guessed who likes women and gold, and they tracked down the missing women. They interviewed one survivor of a Dragon attack, who had been attacked in her plane, with her boyfriend, but they had seen a giant bat-like shape fly past, and caused them to crash. They found out the girl wasn't a virgin and thus hadn't been attacked or kidnapped.
So, the Winchesters tracked the missing women, but were ambushed by the Dragons, who morphed into rugged-looking human males. They attacked the brothers but Sam killed one Dragon, with the Sword of Bruncvik, a Medieval sword that had been forged in Dragons' blood. This was the reason Dragons had lived so long - the only way to kill a Dragon was to kill it with a blade mixed in the blood of another Dragon. Dean wounded another Dragon, and they asked them where they'd found the blade. Dean mockingly said "EBay."
The other surviving Dragon morphed into its Dragon form and flew off. This makes them one of the only monsters the Winchesters have never fully stopped. The Dragon that fled linked up with the third living Dragon who chastizes him but tells him that he managed to collect enough virgins so their goal is still in motion. The two Dragons took a young woman and dragged her to a cliff, and recited a spell to open Purgatory, to free Eve. Bobby Singer had worked out their plan, but he didn't know their true goal, he thought either they were throwing some offering in or releasing something from Purgatory. Needless to say, the Dragons watched as the portal opened, and they threw in the screaming woman, who became possessed by Eve. The Mother of Monsters ascended to Earth, and ordered her offspring Dragons to start a war against humanity.
- The Dragons having a human form would have been explained in one deleted scene in the episode, presumably set during the Winchesters' attack on the sewer base. The Dragons would've claimed that "Your village was attacked and burned to the ground. Who would you say did it? Me, a man? Or a giant monster?"