This one’s a bit confusing. First of all, we’re not talking about a grounded plane which is what happens when a 737 has engine trouble. That’s another whole thing.
A ground plane, at its simplest, is a large piece of metal, larger than the wavelength of the signals that pass through it. It’s sometimes connected to a ground wire or to the earth itself. It’s used for a number of different things.
In the case of a receiving antenna, a ground plane is mounted parallel to the earth that functions as a reflector and makes the antenna itself more useful. In this case the ground plane doesn’t need to be connected to anything in order to work.
In circuitry, a ground plane is a large metal area on a circuit board that serves as the negative terminal for a large number of electrical connections. In that case it generally does get connected to a ground wire through the case or other components, but that isn’t mandatory as long as the circuit is designed not to need a grounded connection.
In commercial applications, a ground plane is a large piece of metal that’s used as a backboard for connecting a lot of different components. That one piece of metal is bonded to the building’s ground system, and as long as the components on it are making a metal-to-metal connection to that ground plane, then everything is properly grounded. It’s a lot easier than running individual ground wires from a whole bunch of individual components to a central grounding block and then to the building’s grounding system.
A ground plane does not have to be special, it just needs to be a big chunk of conductive metal that things connect to. In the case of commercial applications, you’re not dealing with broadcasting frequencies so the actual size doesn’t matter, as long as it’s big enough for the things you connect to it.
One perfect use of a ground plane is a satellite headend system. In a headend system, the multiswitches, splitters, and other small bits are all connected to a ground plane. Typically these things would have been mounted to plywood in many installs but using a metal ground plane instead is an easy way to make sure everything is properly bonded without spending a lot of time.
Thanks to Signal Pro Ashley for this tip!