Regat's physical appearance is not known, but it may be surmised she resembled her daughter and granddaughter, and that she had red hair and possibly green eyes, evocative of the sea.
Queen Regat oversaw the presentation of suitors for the hand of Princess Angharad, and strictly enforced her daughter's adherence to long-standing tradition regarding the magical powers of those suitors. She told Angharad: "You may wed the one your heart desires, and choose your husband freely -- among those, naturally, with suitable qualifications."
Angharad's heart, however, desired an entirely unsuitable non-enchanter, Geraint. When Regat forbade the union, the Princess and her charming suitor eloped and fled Caer Colur. This non-traditional elopement seems to have led to the fall of the ancestral fortress and its ensuing abandonment. It remains unclear whether Angharad's flight directly caused the detachment of the castle from its foundation rock and subsequent floating out into Mona Bay, or whether some other event -- perhaps a magical attack by Achren? -- occurred instead.
Regat's precise fate remains unknown, though it can be surmised that she had perished some time prior to the start of the series, since Eilonwy is described as being the last of the Daughters of Llyr.