covered utensil
盒 centers on a container with a lid: a covered utensil used for holding or serving food or other items.
盒 combines 合 (fit, join) with 皿 (dish, plate), suggesting a dish with a fitting lid. The historical development is straightforward, though the exact ancient usage is uncertain.
The top 合 means 'fit' or 'join', and the bottom 皿 is a dish. Picture a dish with a lid that fits perfectly, making it a covered utensil.
For コウ, imagine a covered utensil holding a hot coal: coal -> コウ, and the lid keeps the heat inside.