a curved lie that tricks air into holding the whole machine up
means a paired limb or surface that birds, insects, and aircraft use to generate lift and stay aloft — or, by extension, a side part that branches off from a main body, like the wing of a building or a political party.
from From Old Norse vængr, the word for a bird's flight-limb, which English borrowed in the early Middle Ages and used to push aside the older native term (Old English had fether-related words for the same thing). From the literal bird-wing, the sense spread outward like the thing itself: the wings of a stage, an army's flank, a building's extension, all named for the way they reach out from a central body. The verb 'to wing it' is much later, an early-20th-century theatre phrase, said to come from actors learning their lines in the wings just before going on.