Barberus Bragge was Chief of the Wizards’ Council in 1262.
Bragge attended a Quidditch match in 1262 and offered 150 Galleons to whomever caught a Golden Snidget which he released onto the pitch (at that time, 150 Galleons was the equivalent of over a million Galleons today). Madam Modesty Rabnott of Kent took to the field in protest at the abuse of the small, defenseless bird; she caught the Snidget with a Summoning Charm and was fined 10 Galleons. This incident began the practice of catching a live Golden Snidget as part of the game of Quidditch (QA4).
Bragge appears on a Famous Wizard card because his actions changed the game of Quidditch forever (fw).
"Barberus" = similar to "barbarian" and "brag" means to boast about oneself. Each of these words suggest his character, which is bullying and crude.