A brut is a Welsh word for a history of the Isle of Britain. Specifically, it is used when this history traces the origins of the island and its first inhabinates--the Britons, who we now call the Welsh--back to the eponymous legendary founder Brutus, grandson of Aeneas.
According to these histories, the island was settled by the followers of Brutus, who was exiled from Rome after accidentally killing his father. Upon arriving on the island, he killed the giant Albion, who previously had given his name to the island, and then named the island for himself--"Brut" becoming "Britannia" in Latin. The earliest known version is the Historia Brittonum, a Latin work. The first "brut" (IIRC), though, was the Welsh translations of Geoffrey of Monmouth's The History of the Kings of Britain, called the Brut y Brenhinned in Welsh. Geoffrey's history starts with the settlement of Brutus, up through the reigns of King Arthur and Cadwaladr Fendigaid.
The word brut was then applied to two epic poems--Robert Wace's Brut (in Anglo-Norman) and Layaman's Brut (in early Middle English), both of which begin their poems with the coming of Brutus, and end with the death of King Arthur. The word brut then began to be applied to the title of any history, not only those which refered to Brutus--such as the Brut y Tywysogion (Chronicle of the Princes) and the Brut y Saesson (Chronicle of the Saxons), both found in the Red Book of Hergest.
From what I can tell, though, the term brut specifically refers to a history of the Island, while the term hanes is more general, refering to people as well as nations.