Fish fingers (aka fish sticks[source needed]) were a type of human food. They were made from fish cut into rectangles, covered in breadcrumbs, then heated up.
Not long after regenerating, the Eleventh Doctor found some frozen fish fingers in Amelia Pond's kitchen, along with some custard. He decided to eat them together as fish custard. (TV: The Eleventh Hour) Fish fingers and custard became an important part of the Doctor's friendship with Amy and Rory.
Later, the Doctor compared House's penchant for eating TARDISes to enjoying processed food like fish fingers. The Doctor's TARDIS, temporarily in human form, expressed puzzlement about what fish fingers were ("Do fish have fingers?"). (TV: The Doctor's Wife)
A faction of Ice Warriors developed a taste for frozen fish fingers (which were the closest thing to their natural diet) during a period of exile on Earth. (AUDIO: Thin Ice)
After Jason Kane's funeral, Peter Summerfield asked Benny if he could have fish fingers. (AUDIO: The Wake)
Benny enjoyed fish finger sandwiches and mentioned them to Leonidas, who decided to try to make one for her. He was reminded by Craisus that fish did not have fingers. (AUDIO: Private Enemy No. 1)