Who is Elayne Trakand from A Crown of Swords and what is their importance?

Elayne is an Aes Sedai, although very young for one. She is accused of being an impostor by Reanne. Elayne is also the daughter of the queen, Morgase. Elayne is to be Queen in a short period of time, but she is off finding the Bowl of the Winds, unknown to Rand. Elayne is one of the women who Rand is in love with.

Elayne eventually takes control of the Aes Sedai and she goes to convince the Kin, also called the Circle, to come and join the rebel Aes Sedai and that they will all have a chance to try again to be Aes Sedai.