A Blight
A Blight (capital 'B') is the term given to the event of the darkspawn corrupting one of the Old Gods and rising with it to the surface world. While darkspawn can occasionally be found raiding on the surface world, it is not termed an actual Blight unless an Archdemon leads them.
The blight
The blight (lower case 'b') is the disease spread by the darkspawn. It twists and corrupts all living organisms, creating such abominations as blight wolves and ghouls (assuming the creatures manage to survive the initial phase of the infection in the first place). These creatures are not actually related to the darkspawn, and their illness always proves fatal, usually in weeks or months of contracting it.
With each passing day, a blight grows. The earth itself withers and dies; the land is leeched of moisture, turning everything dry and brown. The sky fills with rolling, black clouds that block out the sun, making it easier for the darkspawn to surface. As this wasteland spreads, the corruption of the blight spreads with it, diseasing all in its path.
The History of Blights in Thedas
The Blight - Artwork
The Chantry teaches that it is the hubris of men that brought the darkspawn into Thedas. Mages sought to usurp Heaven, but were cast out, twisted by their own corruption, only to return as monsters, the first of the darkspawn. They plague the underground caverns and tunnels once inhabited by the dwarven kingdoms. These caverns and tunnels are called the Deep Roads and extend through out Ferelden. When they discover one of the Old Gods, ancient dragons slumbering in the depths of the earth, it rises as an Archdemon to lead the darkspawn as they spread like locusts across the surface of the lands, destroying all in their path, a Blight. It has been four centuries since the last Blight, but the darkspawn are amassing once again.
The First Blight: Occurred in the Tevinter Imperium, and was supposedly led by the Archdemon version of Dumat, leader of the Old Gods. Though it was eventually defeated, the Blight left the Imperium severely weakened, making it easy for the barbarians who invaded not long after (led by Andraste) to push the Imperium back. Furthermore, in the aftermath, the darkspawn fled into the Deep Roads, nearly eliminating the dwarven empire in the process and on the surface, the Grey Wardens were created as an organization to combat the Blight.
The Second Blight: No information yet.
The Third Blight: No information yet.
The Fourth Blight: No other information other than that it was soundly beaten with the hero Garahel defeating the Archdemon at the Battle of Ayesleigh. Afterwards, the rulers chose to tell the people that the Blight was forever defeated as a way to restore order. No other Blight would occur for 400 more years, so the belief that the Blight is forever gone is common among the people of Thedas.
The Fifth Blight: The current Blight that occurs in Ferelden. It is the first Blight that has occurred as far south as Ferelden.
If the myths about there being seven Old Gods are true, and no Blight has featured more than one Archdemon rising, then it is entirely possible that there are at least two more Blights that Thedas will have to endure before all of the Old Gods have been accounted for.