Orange fruit of late autumn. Some kinds are crisp like an apple; others must ripen until jelly-soft, or their tannins pucker the mouth. Many are pressed flat and dried into sugar-dusted persimmon cakes.
To pick the soft persimmon to squeeze (to bully the weak).
Tips
culture
柿子 symbolizes good luck in Chinese culture because 柿 sounds like 事 (matter/affair), so persimmons represent 事事如意 - 'may everything go as you wish.' They're popular gifts and decorations.
usage
捡软柿子捏 (pick the soft persimmon to squeeze) is a common idiom meaning to bully the weakest target. You'll hear 别拿我当软柿子 - 'don't treat me like a pushover.'