the formal vest that survived its sleeves and became pure swagger.
means A close-fitting sleeveless garment worn over a shirt and under a jacket, typically buttoning down the front and forming part of a three-piece suit.
from A plain compound of "waist" plus "coat" — literally a coat for the waist — dating to the 17th century, when it described a far longer, sometimes sleeved garment than today's trim vest. The pronunciation famously drifted: many older British speakers said "weskit," a worn-down spelling-be-damned form that survived for centuries before the careful "waist-coat" reasserted itself. "Waist" itself traces back to Old English and the idea of where the body "grows" or swells; "coat" comes via Old French "cote" from a Germanic root for a garment.