The subject of this article originates from non-canonical sources. To find out about what is considered "canon" see LOTR:Canon.
Doof is a type of goblin guard in a theater adaptation of The Hobbit, by Edward Mast. In the play, he is one of two goblin guards, (the other being a goblin named Dork.) Doof's job was to basically torture, harass, and make sure that the three Dwarves he was guarding did not escape. The Dwarves he guarded were Gloin, Bombur, and Thorin Oakenshield. In the play, he and Dork get into an argument over a sandwich, and Doof ends up beating Dork over the head with a club, knocking him unconscious. Then, Bilbo, who had not been captured by the goblins, puts on the ring and becomes invisible. The hobbit then sneaks over to the unconscious Dork, takes his club, and hits Doof in the head with it. This knocks him unconscious also. Bilbo then frees the three Dwarves and proceeds to find the other ten. Later, Doof is one of the many goblins to participate in the Battle of Five Armies, where he is killed.
NOTE- Doof only appears in the play adaptation of The Hobbit, and is not considered Canon.