Gobbles was originally owned by farmer Carl Denkins, but was bought by Kyle Broflovski and Timmy because Denkins was going to kill him. They were looking for an entertaining turkey for the school Thanksgiving play, so Gobbles took up this role since they had spent all their budget.
He was named Gobbles by Timmy. Cartman and the other students consequently didn't like him for his lack of capability and unusual appearance. However, Timmy quickly formed a close bond with Gobbles and he even jumped in front of the turkey and took a bullet when Jimbo Kern and his shooting companions tried to kill him.
With Timmy's training, he ends the play by "jumping" the flaming hoop of fire, instead of the professional turkey, which was shot and killed.
Gobbles is a turkey who has a neck problem. He is unable to lift his head for very long so consequentially is neck is always close to his feet. Ironically, this saves his life from a turkey slaughterhouse in the episode.