From the Glossary of The Wheel of Time

(1.) The title of the leader of the Aes Sedai. Elected for life by the Hall of the Tower, highest council of the Aes Sedai, which consists of three representatives from each of the seven Ajahs. The Amyrlin Seat has, theoretically at least, almost supreme authority among the Aes Sedai. She ranks as the equal of a king or queen .

(2.) The throne upon which the leader of the Aes Sedai sits.