Case of 15 Persimmons.  Persimmon is an orange tomato-shaped fruit that is native to Asia (particularly Japan and China) with increasing popularity in the United States. If you've never had a persimmon before, you may be wary of how it will taste. Depending on the variety, persimmons can be astringent or non-astringent. If you enjoy their mild sweetness, persimmons can be a healthy way to introduce more variety to your fruit intake.