Something that took me some hard lessons to learn:
A ground plane in itself is not low impedance. If it was, we could market copper foil as ultra-low-impedance wire.
A closed circuit formed from a conductor close to a ground plane, AND the ground plane, can be very low impedance, though: it is equivalent to a very closely spaced pair of wires that perfectly follow each other's path, which is the lowest impedance circuit possible compared to anything with more spacing (loop area, which is a key ingredient in building coils!) between the conductors. The path of an AC return current in the ground plane will actually mostly follow the path of the conductor above it, since it is the path of least reactance.
Ground bounce is what happens when an RF (or fast rise pulse) signal causes a voltage drop across the reactance of the ground path, so we will minimize it by a ground plane design.
Since this tends to keep the return paths out of each other's way (compared to discrete ground wires, were it will be often the smallest loop and not the assigned ground wire carrying the current!) even though they are galvanically interconnected, you will also lessen the effect residual ground bounce will have, since the reactances the voltage drops occur across are not shared - especially not shared between circuit sections handling amplifyable and amplified signals.
Additionally, if a ground plane AND a power plane are used, they form capacitor plates, acting as one of the best RF filter capacitors available.
Additionally, having currents flowing in shortest loops possible lessens problems with parasitic transformers and also EMI.
Additionally, ground planes make good shields.