A trademark used for underwear. This trademark often occurs in lowercase in print: “The venerable white-underwear company . . . had dabbled
in socks, sweats, and fashion skivvies” (Advertising Age). “About 500 yards away, on three destroyers snubbed up to the dock, men were clambering on the deck
in their skivvies” (Smithsonian).
I've got my skivvies in a bunch.