Not in my dictionary, I found this Wikipedia definition: A historical arbitration, mediative and judicial role in Gaelic culture. Brehons were part of the system of Early Irish law, which was also simply called “Brehon law“. Ireland’s indigenous system of law dates from the Iron Age. Known as the Brehon law, it developed from customs which had been passed on orally from one generation to the next. Brehon law was administered by brehons. Similar to judges, their role was closer to that of an arbitrator. Their task was to preserve and interpret the law.
The brehons of ancient Ireland were wise individuals who memorized and applied the laws to settle disputes among members of an extended family. Some brehons were attached to clans, and were allotted a portion of land for their support. Others lived independently by their profession. They were recognised as a professional class apart from druids and bards, and became, by custom, to a large extent hereditary.
The preparatory course of study extended some twenty years. The Brehon laws were originally composed in poetic verse to aid memorization. Brehons were liable for damages if their rulings were incorrect, illegal or unjust. When one brehon had adjudicated on a matter submitted to him, there could be no appeal to another brehon of the same rank; but there might be an appeal to a higher court, provided the appellant gave security. The ranking of a brithem was based on his skill and whether he knew all three components of law: traditional law, poetry, and later canon law. In pre-Norman times, it was the King that passed judgement, when necessary, following recitation of applicable law and advice from the Brehon. Several dozen families were recognised as hereditary brehon clans.
‘The brehon handed him a hilted weapon.’
Source: Seamus Heaney, Beowulf, 48, and Wikipedia.