She was given in marriage to Matholwch, an Irish King. This caused a spat of troubles as her half-brother EFNISIEN had not been consulted and took umbrage. He caused damage to the king’s livestock and BRAN had to offer compensation.
When BRANWEN produced a son, Gwern, things settled down for a few years, but then she was suddenly banished to the kitchen and treated like a scullion. Here she managed to tame a bird that came after crumbs to become the first carrier pigeon. Only it wasn’t a pigeon but a starling. Nevertheless it made a splendid courier, and when she tied a message to its leg, it made a first class delivery to BRAN.
When BRAN got the news he blew his top, raised an army and rushed it to Ireland. There was one of those battles where just about everyone bit the dust, including BRAN, hit with a poisoned arrow. On his instructions a handful of survivors brought his head home in a magic cauldron (he seems to have had a collection) and he became the notorious Talking Head.
Gwern was killed, EFNISIEN perished and the kingdom was decimated. We don’t know what happed to BRANWEN. Or the starling.