Burdock Muldoon was Chief of Wizards’ Council in the mid-14th century. Muldoon tried to define the difference between a “being” and a “beast.” He decreed that any creature that had two legs was a “being,” and therefore deserving of better representation and treatment. When he called a summit meeting to discuss it, however, the Goblins mocked him by bringing other two-legged creatures such as destructive trolls and hags, mischievous fairies and pixies, and loud disruptive birds such as Diricawls and Fwoopers. After that, Muldoon gave up (FW, FB).
Burdock = a large flowering weed, something like a thistle, with seeds that stick to clothing and animal fur. In fact, the tiny hooks on seeds were the basis for the invention of velcro. The roots are used in a popular drink in the U.K. called Dandelion and Burdock.
The surname "Muldoon" means "hill-fort" and is common in Ireland and Scotland.
Muldoon's tenure as Chief of the Wizards' Council is specifically stated as being in the 14th century in FB. Moreover, he is said in that book to have been followed by Elfrida Clagg, who was Chief in the mid-1300s, a century after the introduction of the Snidget into Quidditch in 1269. However, the dates given on the Famous Wizard card for Muldoon lists him as being born in 1429 and dying in 1490 and serving as Chief from 1448 to 1450, a full century later. This would have made him only 19 years old when he became Chief, which seems unlikely. In the hierarchy of canon, the book trumps the cards, so we list the events of Muldoon's time as Chief in the 14th century and consider the FW card dates to be in error.