She appears at the end of the Eye of the World and at the beginning of A Great Hunt (I think), then I don't believe she comes back. Was this really his mother?
Her name is Kari al'Thor.
According to A Wheel of Time Wiki:
She died when Rand was 5 and he doesn't really remember her.
From the wiki:
"During Rand's confrontation with Ba'alzamon, Kari is used a pawn against Rand. She appears before the Dragon Reborn, surrounded by Fades, who strip and assault her. Rand uses a sword of Light to destroy the Shadowspawn and free her."