A ground plane is a large area of nothing but computer connected to ground. It can range from jsut big enough to sit under an entire IC or to an entire layer on a PCB.
It's basically saying use a huge layer of copper and connect all the grounds to that, rather than running a ground trace all over the PCB. A large conductor has less inductance than a thing conductor.
A ground plane is a large area of copper which either partially or completely surrounds the circuit traces and lands and acts as the connecting path to ground for various components, minimizes stray inductance and provies some degree of shielding from stray EMF. See this image: