The Violet Citadel is the seat of the ruling class of Dalaran, the Kirin Tor. The Citadel hosts the meeting chambers of the Council of Six and the Magus Senate of Dalaran. The Violet Citadel is home to the Grand Library and the Arcane Vault.
The Violet Citadel was built in the early days of Dalaran before it was an independent city. Many towers were added on as the city grew and the mages of the Kirin Tor needed more space. The Citadel was infltrated by Teron Gorefiend to get the the Eye of Dalaran that was located in Arcane Vault. The Citadel was also used as a research facility to study the plague that was sweeping through Lordaeron. Shortly after, the Citadel was mostly destroyed by Archimonde when he leveled most of the city. It took many years of construction underneath the dome, but the Violet Citadel was restored to its former glory. It served as the base of operations for the Kirin Tor during the Nexus War and the War Aganist the Lich King. During the Purge of Dalaran, the Violet Citadel was the location that Jaina Proudmoore imprisoned Aethas Sunreaver before he was rescued by Grand Magister Rommath.
Violet Citadel article on Wowpedia.