My conception of dragons is that they are an ancient race (well... species), as old as or perhaps even older than the race of Men and almost as old as Elves, who were the Firstborn.
They are born of fire and anger and passion, and in their youth they are driven by these things to great destruction. They have no doting parent to teach or guide them, and so they live as animals, predators, for a long time. They are often hunted and killed in this stage (due to the threat they pose to peaceful peoples), so that few live beyond their first few decades of life.
As a dragon grows older, it gains both intelligence and wisdom, similar to any other sentient being. At the very least it will learn cunning, how to hide from hunters and so-called "dragon slayers", lead them into traps and kill them for sport. Sometimes a dragon will learn to communicate with other intelligent races, whether goblins or trolls, Men or Dwarves or Elves. A dragon at this stage may even form alliances for self-preservation and mutual benefit. However a dragon is still a cunning creature, full of the pride of its own strength, and will often betray its allies at an opportune moment.
Dragons continue to grow throughout their lives, and the oldest dragons are therefore also the largest, although not always the most powerful. They eventually lose the power of flight due to their great size, and some may even be unable to crawl or walk very far over land. But their intelligence and wisdom, and their cunning, never lose their potency. And with dragons, it can be truly said that "Age and treachery will win out every time over youth and skill".
The oldest dragons can often be found to have people and creatures of various races worshipping them as gods, dwelling in remote temples, and living off the sacrifices given to them by "lesser" creatures. For the dragon, this is as it should be -- they are clearly the most worthy of worship and adoration of all sentient beings in this middle realm, and thus deserving of whatever praise and honors (and sacrificial food and wealth) come to them.
Of their power, what needs to be said? All dragons can breath fire, and the heat of their fire is proportional to their age and size. While a young dragon can do little more than burn a few trees (or wooden buildings), an older, larger dragon can melt some metals with the heat of it’s flame. The most powerful dragons could cause iron and steel to run liquid in seconds.
Dragons also have the power of glamor in their eyes, which again grows with time, age, wisdom and cunning. This may be what allows them to become worshipped as gods in the later stages of their life, for they can charm large groups of people with the power of their gaze. Experienced dragon hunters know well that they must avoid the eyes of the dragon. Inexperienced dragon hunters often do not survive to learn this lesson.
Finally, older dragons sometimes learn something of magic, usually through the alliances that they form with other (magic-using) people or creatures. But a dragon’s magic is not one of raw destructive power, for they have no need of such. Their interest is in the gathering of knowledge for their own dark designs, foretelling the future, and deceiving others in order to increase their influence. In other words, dragons will use magic in order to increase their appearance as gods, and thus more easily and effectively deceive others into worshipping and serving them.
And that is all I know of dragons thus far.