Growf is a hypothetical sound commonly made by dragons, transliterated phonetically. In much the same way a cat is said to "mew" and a dog "bark", dragons are said to "growf".
The term appears to originate from a relatively obscure character named Growf the Dragon, created by non-Furry artist Phil Foglio, co-author of the Girl Genius comics. The original drawing portrayed a small purple dragon who said "Growf" with an indeterminate expression that might have conveyed a number of different emotions. Growf and his singular vocalization appear to have been adopted by fans of dragons in furry fandom and closely related circles. On Furry-themed MUCKs, some dragon characters have been seen with badges proclaiming them to be a BGD or "Big Growfy Dragon".
Growf still appears on Phil Foglio's official website, Studio Foglio.
Growf is also a foxish sound meaning "no."