There is no mention of a clementine cake in the short story The Secret Life of Walter Mitty. Away from his fantasies he goes to the shop to just buy dog biscuits.
However, a clementine cake is an important motif in the 2013 film The Secret Life of Walter Mitty. His sister Odessa first gives it to him at work at the beginning of the film, saying "Happy birthday . . . Mum made you your favorite clementine cake." He doesn't look very impressed with it and the cake seems to work as a reminder of a boring reality that leaves him unable to express who he really is. When his new boss wakes him up from a fantasy, by flicking a paper clip up at him, the first thing he does is pick up the cake.
Later on in the film, the photojournalist Sean O'Connell leaves instructions on how to find him wrapped around a slice of clementine cake. First it signifies that despite all the craziness, he is still living in reality, and second, it signifies that, as it is only a slice, his boring life is becoming a thing of the past.
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