Aeonar is a secret magical prison located somewhere in Ferelden, a place where suspected maleficars are held, sometimes indefinitely.
The Templars bring those who are accused, but whose true nature cannot be proven. Aeonar is the final, terrible test.
Aeonar was once a magical Tevinter laboratory, but when Andraste died, her disciples overtook the fortress for some reason. They slaughtered all the mages there while they were in the Fade, leaving the Veil pretty much tattered beyond repair. The Veil is so thin in Aeonar that, according to The World of Thedas, Vol. 2, even those without magic can feel demons crowding to get through.