Brân fab Llŷr, also known as Bran the Blessed or Bendigeidfran since the thirteenth century, belongs to the house of Llŷr, both in general terms and in terms of the Celtic Interpretation of mythology. Although many people have pointed to parallels between the character that survives in Welsh literature and Bran mac Febail (and others not associated with the Blessed Isles), the connections have most likely accreted after the Otherworld personality appeared.
Calling Brân the son of Llŷr, is simply calling him the son of the sea. Although, Llŷr was later identified as a vague individual and Welsh tradition offers a full family tree including Brân’s brother, Manawydan fab Llŷr, the original usage merely reflects the Celtic tendency to describe Otherworld places as being beyond or below the waves. In effect, this is creating a conjectured ancestry for an Otherworld animal or their spirit form that had some positive interaction with someone from our reality in an era when ancestry and rank were considered extremely important.
The Brân of the surviving tales is a high king of the Isle of the Mighty (usually Britain or Prydain, but possibly a reference to a region of the Otherworld) and embroiled in politics with the king of Ireland, known as Matholwch. The Celtic Interpretation takes this to indicate something of the intermarriages and conflicts codified in the Irish traditions of the Tuatha de Danaan and the Formorians, along with tensions between the Gaelic speaking and brythonic speaking groups of settlers in the Blessed Isles. That a member of the House of Llŷr is the High King of Britain may also indicate the belief that the Otherworld people (or the Fair Folk) were here first and had an older right.