One of the founders of Borgin and Burkes, a shop in Knockturn Alley. The man behind the counter when Lucius Malfoy came in (CS4), however, was Mr. Borgin.
Burke was one of the people that Dumbledore interviewed when he was piecing together the story of Merope (Gaunt) Riddle. Burke purchased a heavy gold locket from her that he knew once belonged to Salazar Slytherin, paying her 10 Galleons even though he knew it was priceless. Caractacus is described as a small old man with a thatch of hair that covered his eyes (HBP13).
Burke hired Tom Riddle when he was fresh out of Hogwarts to research and "persuade" owners of powerful, valuable magical objects to sell them to Burke. Burke was as surprised as anyone that Riddle vanished one day without leaving word (HBP20).
Skills
Drove a hard-bargain when trading at his shop in Knockturn Alley.
Commentary
Etymology
'Burke'=English for a gruesome murder involving suffocation and dissection. More commonly, "to burke" something is to avoid a problem, usually by stifling it or hushing it up [NSOED].
'Caratacus'=romanized version of the old Welsh name 'Caradog,' meaning "beloved."
From the Web
Pottermore: Pure-Blood and the Sacred 28 by J.K. Rowling