fancy box; decorated box
A box that is decorative or fancy in itself, not necessarily for cosmetics. Often used for gift packaging or elegant storage.
I put the sweets in a fancy box and gave it as a present.
vanity case; cosmetics case
Specifically a box or case for holding cosmetics or toiletries. Often portable.
When traveling, I keep my cosmetics together in a cosmetics case.
Compound of 化粧 (keshō, 'makeup') and 箱 (hako, 'box'). The reading けしょうばこ reflects rendaku voicing of はこ to ばこ.