What is the importance of a ground plane of a PCB?

The term "Ground" should be reserved for just that - the stuff we stick stakes into in order to establish an electrical connection to the earth.

Within a PCB, only occasionally is there a true "Ground" plane - there may well be a Ground used to connect the PCB to the chassis and the power transmission safety earth but this ground generally is found only at the edges of the PCB and perhaps to connector shields in order to provide a safe path to drain electrostatic discharge (ESD) events away from the core circuitry of the PCB.
however I'll refer to the plane in question as "0V".Despite the way we draw schematic diagrams, there is no such thing as a single-ended signal. Currents always need to travel around a loop so when we draw a logic gate, for example, we really only draw half of the circuit. The input of a logic gate is really responding to the difference between the voltage on the trace and the local voltage of the 0V reference level. You'll note that I stipulated the "local voltage" - if there isn't a low impedance connection between the reference levels of the source driver and destination receiver then the received signal difference may well be less than the driver output, since the return current in the 0V line will develop a voltage drop and consequently reduce the noise margin of the logic receiver. So, to minimize the return path impedance, the 0V line is often created as a plane on the PCB.

In considering CMOS logic, it may appear that the super high input impedance of MOSFETs means that there aren't any significant currents to worry about - but this only applies to the DC or steady-state current when there are no transitions on the net. The transition of state involves high frequency currents which do, in fact, return via the 0V net (and/or the power supply net, which at high frequencies is the same as the 0V net when there is adequate decoupling capacitance between the two) or, if there is inadequate coupling between the signal net and pwr/0V then the current may well return via adjacent traces in the form of crosstalk.

On PCBs without room for a whole plane, the 0V line may be sometimes be implemented in tracks, however a couple of critical elements must inform the design. A high frequency current traveling around a loop can make the loop into a marvelous radiating antenna, so the area of the loop must be minimized. This means that the 0V line must be routed close to any tracks carrying high speed signals (remembering that fast logic transitions require very high frequency components). In addition, the 0V line must be scaled for minimum voltage drop for DC currents.

However, when there are more than a handful of high speed signals, in practice a good reference plane (or two, or more) becomes essential. The signal nets may also need to be routed on controlled impedance traces (to eliminate reflections which distort the signal) and controlled impedance traces without a consistent 0V plane are extremely difficult to route - a plane makes the task a lot easier.

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