targaryen "blood of the dragon" being a little more literal.
every so often, a targaryen will become spontaneously pregnant with a dragon egg, or even a clutch if the gods be willing. when the blood of valyeria was still pure, it could be expected to happen to a targaryen every few years. aegon the conqueror himself was known to have laid a few, king jaeherys and alysanne many along with their large number of children. however, as the bloodline diluted by outmarriage and the dragons died out, less and less instances of this have occurred.
the human-born eggs have never hatched into dragons. but still, it is seen as a fortuitous sign for the house when a targaryen swells with an egg, more auspicious still when with a clutch. they are paraded around in court as a sign of their power, sometimes seen as a truer targaryen and/or heir than those ahead of them in the line of succession. daemon blackfyre used his two egg pregnancies to bolster his claim to the throne over daeron the good, whom had none.
carrying an egg is a cumbersome, unpleasant affair, made all the more deadly and terrible by the laying process. the eggs are heavy as stone and hot, like a fire beats inside them. the ridged scales uncomfortable and unyielding as they are pushed out. the maesters have little experience in assisting targaryens in this matter, as this is the blood magic of old valyria. some have died in the process. yet, still, some targaryens desire to carry, and seek information from the dragonkeepers and old texts to find out how to induce them. and after the dance and death of the last dragon, this became all the more relevant in hopes they may learn to hatch them.
but it was thought that the blood may have become too thin. viserys ii married outside of the blood of old valyria. as had daeron ii and all of his sons. scarcely any eggs have been laid since the time of dragons at all.
that is, until aerion brightflame comes of age and carries an egg with the smug, stubborn pride of a dragon. and then another. and then a clutch. perhaps he has good reason to believe he is a dragon, when he looks upon his small hoard of eggs. if only he can learn how to make the dragons within awake...
