Noble dragons (Draco Nobilis) are intelligent, arrogant, powerful, and graceful and beautiful in a specialized sense. Noble dragons are huge and winged, can produce an extremely hot flame, and seem to defy normal physics in both their flying and their flaming. If they were flesh and blood, each noble dragon would weigh many tons, but the noble dragon that appeared in Ankh-Morpork merely flapped her wings once to take off and glided for the rest of her flight. The noble dragon is not known to eat much in the way of energy-rich fuels, but its flame has been found to be far hotter than that of the most gluttonous swamp dragons.
The fact is, the noble dragon is one of the Discworld species that has evolved to live on magic. Its body materializes by magic, flames by magic, and flies (or glides) by magic. Since the large amount of magic required for a noble dragon to exist in the (somewhat) more normal dimensions of Discworld are not widely or easily available, the noble dragons have gone into another dimension, becoming metaphorically squished up like rather huge and beautiful sardines. A noble dragon can be summoned from that dimension, by a person, or several people, performing a ritual according to The Summoning of Dragons written by the wizard Tubal de Malachite many years ago. People performing this ritual have to imagine the dragon very intensely, and gather objects that might be magical. The noble dragon feeds on the magic, comes through the mind of one of those people, and afterwards may be able to read his or her mind. In practice, the materialized noble dragon comes to share some personality traits with chosen person.
Dragons can also be summoned in the presence of a very intense field of raw magic, like the ones in the Wyrmberg in The Colour of Magic. A very powerful imagination and concentration is also needed. Depending on the imagination of the person and the training, one can summon different quantities of dragons, but they can only keep on existing within range of the Wyrmberg (because of some kind of inverse square law). As the dragons fly away they start to dwindle.