Warning: The following text contains spoilers relating to the plot of Prophecies.
The Academies of the Arcane Arts are famous schools of magic, run by the Order of the Flaming Scepter.
Such Academies are located at Nolani and Drascir. These were known all across Tyria as the most prestigious schools of magic. Ambassadors from Orr and Kryta often made special arrangements to have their children study here, though they were not of Ascalon descent.
The center of each Academy is marked by several magic obelisks. These obelisks seemingly aid mages of the Flaming Scepter order in focusing magic at their location.
The Academies at Nolani and Drascir are connected by a magic portal - as players find out at the end of the mission Ruins of Surmia. It is unknown if there are other Academies (for example at Rin), and if these are similarly connected to the network of portals. Note that the Ascalon Academy at Ascalon City is not an Academy of the Arcane Arts, but a training facility of the Ascalon Army.
Though the Academies at Nolani and Drascir were destroyed by the Charr in the Searing, a few of the Flaming Scepter Mages still guard the ruins, especially to deny the Charr access to the magic obelisks and the magic portals.