Potatoes are a starchy crop, which was originally a wild growing plant. Thousands of years of cultivation and selective breeding resulted in the tasty spuds we know now. It is however unclear whether these particular Potatoes were cultivated by some highly determined farmer, who wouldn't allow the end of the world ruin a good crop. Likewise these could be a now wildly growing breed, which somehow flourishes despite the lack of seasonal care-taking. In either case, someone has plucked them from the ground, cleaned them and then left them lying around for whatever reason.
Potatoes can be consumed to refill the character's Hunger bar by a small amount.