What is the role of zener diode in this clipper circuit?
When Vo is positive, it clips at around 4.6v (3.9v zener + 0.7v diode). Above 4.6v, the zener and diode combined act like a clamp, conducting, to bring the voltage down. R drops the remaining voltage.

When Vo is negative, the diode blocks clipping. No current flows through the diodes. If no current is drawn to/from Vo then voltage across R is zero therefore Vo equals Vi

It's not much of a voltage regulator at all if AC is passed in. It is not possible to say what this circuit could be used for; it could be anything. But in short, it simply limits Vo to about +4.6v.