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The turkey was a type of bird native to Earth. It was used as food by humans, most notably at Christmas. (TV: Children in Need Special, Out of Time, Voyage of the Damned) While Clara Oswald was preparing Christmas turkey for her family, she was forced to use the Doctor's TARDIS to have it ready on time. (TV: The Time of the Doctor)
The Tenth Doctor mentioned to Rose Tyler that having met her mother, nut loaf was a more appropriate dish for Jackie Tyler to cook at Christmas lunch rather than turkey. It was at that joke that she smiled after the Doctor's regeneration. (TV: Children in Need Special)
The tradition of eating turkey at Christmas was misunderstood by apparent Earthonomics expert Mr Copper. He confused the bird with the Earth nation of Turkey. He said that the people of the UK went to war with Turkey every Christmas, after which they would then eat the people of Turkey. (TV: Voyage of the Damned)
Controlled exposure to the Time Vortex could potentially cook a turkey to perfection, but also risked restoring it to life and causing it to lay eggs. The Eleventh Doctor also mentioned that nothing short of a time machine can cook a turkey properly, which extended to the sonic screwdriver not having an "app" for this function. (TV: The Time of the Doctor)