'bandboxy' originates from English, specifically the word 'bandbox', where 'band' meant 'a ribbon or neckband' and 'box' meant 'a container (box)'.

'bandbox' developed in Early Modern English as a compound of 'band' + 'box' (originally a box for bands or collars); the adjective form 'bandboxy' arose by extension to describe the neatness associated with such a well-kept box and then applied to rooms, clothing, or persons.

Initially it referred to a 'box for bands or collars'; over time the sense shifted to the neat, trim quality associated with such a box, and 'bandboxy' came to mean 'very neat or smart in appearance.'