to carry in the bosom or the sleeve, to wrap, to conceal
褱 centers on holding something close and hidden: carrying it in the bosom or sleeve, wrapping it up, or concealing it from view.
褱 combines 衣 (clothing) with 眔, which likely contributes the sound and the idea of enclosing or wrapping. The character originally depicted something held inside clothing.
The outer 衣 is clothing, and inside is 眔, which looks like an eye 罒 over water 水. Picture hiding something precious inside your robe, wrapping it up so only a watchful eye can see it.
For カイ, imagine a spy named Kai who conceals secret papers in his sleeve: Kai -> カイ, and he carries them hidden in his clothing.