The Amyrlin Seat is the leader of the Aes Sedai. Her full title also includes "Watcher of the Seals" and "The Flame of Tar Valon." Among Aes Sedai, she is addressed as "Mother", and she addresses other Aes Sedai as "Daughter."
The Amyrlin Seat is raised from one of the Ajahs, but is subsequently considered to be of "all Ajahs and none", so she can fairly rule over all Aes Sedai. It can be insulting to publicly mention an Amyrlin's Ajah, as it challenges her impartiality.
The Amyrlin Seat is considered to be the most powerful individual in the entire known world. She is considered the social superior of even kings and queens, and is entitled to demand the presence of any monarch, who is expected to give deference to her position.