Victorian Era euphemism, specifically the category of euphemism known as indirection (compare privates, behind, sleep together). First intended meaning was "trousers", attested from 1823. Meaning "underwear" is recorded from 1910.
Strip down to your unmentionables.
Gentlemen don't stare at ladies' unmentionables.
And where's her... unmentionables?
The Hollywood Gossip - Some of these pictures do contain nudity, but the unmentionables are censored out.
Imagine starting with a full one piece swimsuit and cutting away the extra fabric until you're left with the thinnest strips to cover your unmentionables.