pocket, feelings, heart, yearn, miss someone, become attached to, bosom, breast
懷 centers on holding something close within oneself, whether physically in a pocket or bosom, or emotionally in the heart. The meanings of yearning, missing someone, and becoming attached all grow from this idea of keeping something cherished inside.
懷 combines 忄 (heart/mind) with 褱, which likely contributes both sound and the idea of wrapping or enclosing. The character expresses holding something within the heart or bosom. The modern Japanese simplified form is 懐.
The left side 忄 is the heart, and the right side 褱 looks like something wrapped up and tucked away. Picture your heart wrapping around a treasured memory, keeping it close like something in a pocket.
For カイ, imagine a person named Kai who keeps a photo of a loved one tucked inside their pocket over their heart: Kai -> カイ, and the pocket holds the feeling close.