A ground plane in PCB assembly is a layer of copper that appears to most signals as an infinite ground potential. This helps reduce noise and helps ensure that all integrated circuits within a system compare different signals' voltages to the same reference potential.
It also serves to make the circuit design easier, allowing the designer to ground anything without having to run multiple tracks; the component needing grounding is routed directly to the ground plane on another layer.
Ground planes can also be placed on adjacent layers to power planes creating a large parallel plate capacitor that helps filter the power supply.
Ground planes are sometimes split and then connected by a thin trace. This allows the separation of analog and digital sections of a board or the inputs and outputs of amplifiers. The thin trace has low enough impedance to keep the two sides very close to the same potential while keeping the ground currents of one side from impacting the other.