She's the daughter of the goddess Dôn and a mortal named Beli Mawr, and half-sister to the sorcerer Gwydion, the god Amaethon, and the smith-god Gofannon.
Consorts and Children:
Despite being a virgin, she once gave birth to two sons, a sea-being (possibly a merman) named Dylan ail Don and a shapeless blob that eventually formed into a boy that grew twice as fast as normal, named Lleu Llaw Gyffes (meaning 'fair-haired' with a 'skilled hand'). Embarrassed by Lleu, she cursed him so that only she could name him (which she refused to do until she was tricked), he could only receive weapons from her (though, again, she was tricked), and he would never take a human wife (he eventually found a way around this). She also has two more sons, who accompanied her half-brother Caswallan in his pursuit of Julius Caesar.
Notable Stories Involving Her:
Her name means 'silver wheel', which connects her to the moon and stars, but also connects her to the wheel of the year. She lives in the Corona Borealis, in a palace called Caer Sidi, meaning 'revolving castle'. The souls of the dead are said to wait there for her to decide their fate before they're reborn into their next life.
She's said to shapeshift into an owl, and through its eyes, see into the human subconscious.
Arianrhod Around the World:
Her Greek and Roman equivalents are Artemis and Diana, respectively, though she also could be considered the Celtic counterpart of the Norse goddess Freyja.
SOURCES: Wikipedia, Encyclopedia Mythica, GodChecker, Goddess Guide, & The White Goddess