Valyrians owe their power to the fact that they have an ability to bond with and ride dragons. They are also more tolerant to extreme heat and high temperatures than other races.
For five thousand years, the Valyrians were a great power thanks to the dragons.
Four hundred years ago, Valyria was completely destroyed in what is today called the "Doom" when a string of volcanoes erupted and completely destroyed the city.
After the destruction of Valyria, the Targaryens set their sights on Westeros and, with the help of their three dragons, spearheaded an attack that brought six of the existing seven kingdoms, unified under King Aegon I. The seventh kingdom, Dorne, joined the kingdom through a political/marriage alliance two centuries later. The Targaryens ruled for approximately three centuries until the reign of Aerys II (the Mad King), when his son Rhaegar kidnapped Lyanna Stark (Ned Stark's sister) of Winterfell for unknown reasons. This started a massive uprising led by Ned Stark, Robert Baratheon and Jon Arryn.
Generations of in-breeding have preserved in the Targaryen bloodline the classic Valyrian features of silver-white (platinum blond) hair and very fair, pale skin.