Hi John and all,
The most common type of ground plane antenna is a quarter wave electrical length which believe it or not works out to a half wave. Picture this, a quarter wave radiator mounted on the ground with a phantom quarter wave below ground making it a half wave. Naturally this is electrical theory and not actual practice. AM broadcast towers are usually quarter wave ground mounted (ground plane) radiators so it's pretty easy to visualize.
Now raise the radiator above ground and add 3 or 4 quarter wave radials, electrical ground above actual earth ground and you have a ground plane antenna. I suppose it's easier to understand if you think of it as "the plane of electrical ground" geometry.