That is Solanum mammosum, a member of the nightshade family and a relative of the tomato and potato. Although it’s sold widely in Japan from September to November, it’s actually a native of South America, where it grows as a perennial shrub. It is now grown commercially in Japan, but because of our cooler climate it’s strictly an ichinensei shokubutsu (annual plant) here. The fruit is poisonous and the stems are prickly, but growers usually remove the leaves and thorns before they ship the branches to market.
Now let’s talk about common names. I’ll leave you to speculate why this might be, but whoever came up with the Japanese names ignored the obvious. I mean, even the taxonomist who assigned the Latin name had boobs on the brain. But in Japan, breast imagery was bypassed in favor of…eggplants. Here, the plant is known as tsunonasu (horned eggplant), kanariyanasu (canary eggplant) and kitsunenasu (fox eggplant). This last one is because if you look just right at the protuberances on the fruit, they resemble the pointy nose and ears of a fox.