How does EMI affect a circuit?
having a dedicated GND/Vcc plane has dual benifits. 

1) It acts as a thermal spreader thereby acting as a natural coolant for your PCB.

2) Reducing EMI. 
All signals are referenced to GND on your board. Having a constant ground plane below your signals gives you a clean signal. Another advantage of having GND planes is that they sink in EMI generated by high noise generated sections. Imagine you have tracks ,say on the edge. Suppose there is interference from other sections of your system. It corrupts the signals of those tracks. But if you have a GND pour/layer shielding it the GND absorbs the EMI thereby nullifying its effects.
In other words the GND plane acts as a shield that sink EMI.

Many antenna vendors recommend a GND pour (Stitched) near the antenna section.