Mortification of the Spirit is a penance where the victim is embarrased, frightened, etc., while not in a real danger to herself.
Moiraine Damodred imposed the Mortification of the Spirit unto herself after being newly raised to the shawl because she thought about using the Amyrlin's death to her own use. During the murdered Amyrlin's funeral, Moiraine wore clothes that were revealing to her Cairhienin sensibilities. The way the other attending Aes Sedai looked at her created intense embarrasment for Moiraine, thus fulfilling the goal of Mortification of the Spirit.
Common to contrary belief, Aes Sedai are not perfect. In fact, they rarely are. When Aes Sedai make severe mistakes, they often submit themselves to the Amyrlin Seat, who decides on the Aes Sedai's penance depending on the person and the circumstances. Some Aes Sedai, however, are very peculiar in a way quite similar to the Aiel ji'e'toh. These Aes Sedai set a penance for themselves, often undergoing Mortification of the Flesh, Mortification of the Spirit, or a regular penance at a farm, etc. Once having undergone this experience, it is believe to "cleans their souls" of their mistake.