A persimmon is the edible fruit of a number of species of trees of the genus Diospyros in the ebony wood family (Ebenaceae). The word persimmon is derived from putchamin, pasiminan, or pessamin, from Powhatan, an Algonquian Cree and Mohican) of the eastern United States, meaning "a dry fruit". Persimmons are generally light yellow-orange to dark red-orange in color, and depending on the species, vary in size from 1.5-9 cm (0.5-4 in) diameter, and may be spherical, acorn-, or pumpkin-shaped. The calyx often remains attached to the fruit after harvesting, but becomes easier to remove as it ripens. They are high in glucose, with a balanced protein profile, and possess various medicinal and chemical uses. While the persimmon fruit is not considered a "common berry" it is in fact a "true berry" by definition.
They have a deliciously musky flavor, somewhere between a mango and a fig; they are a sticky-sweet delicacy that looks like a tomato, but eats like a pear. Even better, you can cut them up and they don't darken like bananas and so retain their gorgeous color in vegetable or fruit trays. You find a lot of recipes that call for the persimmon pulp like cookies, cakes, and puddings.
There is a catch to this delectable fruit: eating too much unripe persimmon has been linked to forming indigestible clots in the stomach and intestines.
Unripened persimmons contain the soluble tannin shibuol, which, upon contact with a weak acid, polymerizes in the stomach and forms a gluey coagulum that can affix with other stomach matter. The Merck Manual of Diagnosis and Therapy notes that consumption of persimmons has been known to cause bezoars that require surgery in over 90% of cases.
So, go ahead and enjoy ripe persimmons, but -- as always -- in moderation.