The Valyrian Freehold was the empire established by the Valyrian civilization in the continent of Essos, centered around the city of Valyria in the eponymous peninsula.
Thought to initially be a modest community of shepherds, the Valyrians rose to prominence after the discovery of dragons, in the volcanic area known as the Fourteen Fires. Having tamed the mighty beasts, the Valyrians were able conquer their surrounding lands and began a westward expansion.
The Ghiscari Empire, however, sought to halt Valyrian expansion and declared war on their neighbors from the opposing shore of Slaver's Bay. Ghiscari legions attacked five times but were defeated. The Freehold's forces then marched on the Ghiscari capital, Ghis and laid waste to it, leaving little more than a smoldering ruin behind and nearly erasing Ghiscari people and culture from history.
Afterward, the Valyrian Freehold became the dominant civilization in the known world, with its own language, religion and customs. The Freehold founded a number of colony cities, connected by a network of roads all of which led back to the capital city.
For nearly five thousand years, Valyrian supremacy remained uncontested. However, a cataclysmic event known as "The Doom" laid waste to the Valyrian capital, its people, and the surrounding lands. The Valyrian peninsula itself was shattered and the ocean came sweeping in, becoming the Smoking Sea. Dragons, as well as Valyrian recorded history, spells, and knowledge were lost. With its center of power destroyed, the empire collapsed. And of the mighty families of dragonlords who ruled the Freehold, only one survived, House Targaryen, which had established on Dragonstone years before the Doom.
In the books
In A Song of Ice and Fire, the Valyrian Freehold was ruled, nominally, by all "free holders" -- freeborn landowners -- had a say in its governance. In practice, however, forty families of great wealth, high birth, and strong sorcerous ability, known as Dragonlords, tended to dominate. The Targaryens were one of these families, but far from the most powerful.
The Freehold not only conquered the Ghiscari Empire, but also the Rhoynar people established around the Rhoyne river, leading to their exodus across the sea to Dorne. The modern Free Cities, as well as several others, were established as Valyrian colonies and became independent after the empire was shattered. The major exception to this is Braavos, located in the extreme northwest of Essos, which was founded by escaped slaves who fled Valyria, and remained hidden even long after the Doom. Braavos is thus sometimes referred to as the Bastard Son of Valyria.