The Flame is an ancient symbol, though its original meaning has been forgotten by present-day people.
In the Age of Legends, the Flame, along with the Dragon's Fang, was part of the ancient symbol of the Aes Sedai. Since the Breaking and the splitting of the Aes Sedai to remove the men, the Flame has taken on another meaning. It is no longer connected with female channelers by the common person, and its origins are lost to common knowledge by the passing of years, but superstition still regards the Flame as a sign of female Aes Sedai.
In the Last Battle Egwene al'Vere, while battling M'Hael, creates a new weave as a direct counter and opposite to balefire—a weave of pure creation as opposed to balefire's pure destruction. She calls it the "Flame of Tar Valon". This "Flame" cristalized Mazrim Taim from inside out like freezing in ice when he was hit. A multihued, beautiful crystal grew from him, uncut and rough. Somehow Egwene knew that the Flame would have had much less effect on a person who had not given himself to the Shadow.
Egwene dies with hitting everything around her with the Flame of Tar Valon. As a consequence the entire area which was badly damaged by Taim got covered like a blanket of crystals coated the ground, filling all cracks with crystal and healing them including the Sharans frozen into the crystal. Egwene herself turned into a giant pillar of crystal column, wide as an ancient leatherleaf tree, rising some fifty feet in the air having Vora's sa'angreal frozen in its center.