The invisible plane represented the "invisible" feminine compliance that women of the Depression Era had to rely on in order to survive in the hostile male dominated work place.
The Invisible Plane was a creation of Diana's during her younger years on Paradise Island. She created it to be an improvement on her mother's planes which would be shot down in Man's World. The result of her innovation was an invisible plane that could fly at terrific speeds silently and not be detected by hostile forces, thus avoiding unpleasant conflict. Initially, it was described as being transparent.
Wonder Woman continued to use the plane for super-speed, outer space, and mufti-dimensional transport up until the un-powered era of Diana Prince. Thanks to tinkering by gremlins, the Plane even developed intelligence and the power to talk. (Wonder Woman Vol. 1 #312)