The title of P.G. Wodehouse's short story "The Custody of the Pumpkin" is justified by the author by making the tending and care of an award-winning pumpkin the sole focus in the life of Lord Emsworth at that point.
A rare and massive specimen of its kind, the pumpkin is named by Lord Emsworth and his gardener Angus McAllister as "The Hope of the Blandings". This alone is comical considering that the Blandings constitutes a very rich and powerful estate for which really there is no need for "hope". Moreover, the obsession of Lord Emsworth for the pumpkin's well-being is part of the satirical traits that Wodehouse brings out about the aristocrats of his time.
The actual importance of the pumpkin is simply that it would make Lord Emsworth happy to win the competition. Considering that he has no other interests in life (with the one exception of his huge, prize-winning pig), winning the contest is, in his eyes, a huge feat.