So you don't want me to ask about a ground plane independant one then
I knew you would...
The first thing to consider is that the Earth (as in planet) is considered the ultimate ground, or if you will, the perfect
zero potential. That is, any potential NOT zero is referenced to earth (ground).
This is true for any potential in wires, antennae, clouds, YOU, etc..
Now, take something "electrically" isolated from ground (Space station, airplane, handheld radio, etc.). In order for a radio to work, for instance, especially in transmitting mode (and to a lesser but not insignificant way, receiving), there needs to a ground as part of the system. And, in most cases, the more ground, the better. For convenience, this is often called the "ground plane" when speaking of electromagnetic wave transmission.
Take, for instance a car. Rubber wheels, right?, Very nice insulation from electrical ground). Now most cars have enough steel that that can represent enough of a ground to satisfy the needs of the radio, GPS, OnStar, etc. But what of a Corvette? Not nearly as much steel, and certainly in the older ones, very poor AM and FM reception (of this I know: I had a new '69 and now have a '74). So the solution was to attach a 1/4X4X4" metal plate to the ground lead of the antenna (directly beneath it, proximity to the antenna is critial) to improve the cars radio system's "ground plane" and, therefore, performance.
There are lots of other schemes for improving a system's ground plane (radial ground leads, for instance) but the reasons for doing this are all the same.